SPINA, J.

A jury in the Superior Court convicted the defendant, Marion Szlachta, of murder in the first degree on a theory of extreme atrocity or cruelty for the beating death of his housemate, Randy Lee Maleski, on July 8, 2008.1 At trial, the defendant conceded his guilt of murder, challenging only whether he was guilty of murder in the first degree or in the second degree. He sought a verdict of murder in the second degree on the ground that his impaired mental condition affected his ability to make decisions in a normal manner or to appreciate the consequences of his actions. Represented by new counsel on appeal, the defendant contends that the judge erred in refusing to give the defendant's requested jury instruction on mental impairment. The defendant asserts that we should exercise our extraordinary power pursuant to G. L. c. 278, § 33E, to reduce his conviction to murder in the second degree. For the reasons that follow, we affirm the defendant's conviction and decline to grant relief under G. L. c. 278, § 33E.

1. Background. The jury could have found the following facts. We reserve other details for our discussion of the specific issues.

In late 2007, the defendant, who also was known as "Mombo," moved into a room in the basement of a one-story home owned by Daniel Bouchard on Trafton Street in Chicopee. The defendant had been "thrown out" of his apartment, where he had lived for approximately fifteen years, and had lost his job as an electrician, work that he had done for approximately thirty-three years. The defendant knew Bouchard and his family because he had dated the sister of Bouchard's wife for several years. Bouchard charged the defendant fifty dollars per week in rent, and the defendant helped to perform household chores. Also living in Bouchard's home was the victim, the brother of Bouchard's wife, Katherine. After Katherine died in February, 2008, Bouchard, the victim, and the defendant continued to live in the house together.

Sometime in June, 2008, the defendant left the house for several days and did not mention to Bouchard where he was going. During the defendant's absence, Bouchard found a note in the kitchen that was signed "Mombo" and that stated, "Sorry Dan. Either this or hurt Randy. Thanks for everything." Bouchard could not recall whether he and the defendant had a conversation about the import of the note after the defendant returned.

On July 8, 2008, Bouchard left the house for his job with the water department of Chicopee at approximately 6:30 A.M. He returned home for lunch around 11:30 A.M. and spent some time talking with the defendant at the kitchen table. When Bouchard left the house to return to work, the defendant was still in the kitchen, and the victim was working on his fishing pole on the rear deck of the house.

Bouchard returned home from work that day just after 4 P.M. When he entered the front door and walked into the living room, he noticed that the wooden chair at the computer table had been knocked over. Bouchard proceeded into the kitchen and saw the victim lying face up on the floor between the door to the basement and the back door of the house. He was bleeding from his nose and mouth. Bouchard placed a 911 telephone call, returned to the victim to check for a pulse, and, when he did not feel one, placed another 911 call and then went outside to wait for emergency personnel. Fire department paramedics were first on the scene, and they determined that the victim was dead.

Officer James Gawron of the Chicopee police department then arrived at Bouchard's house; he conducted a sweep of the first floor but did not find anyone. He chose not to enter the basement because the victim's body was lying right next to the basement door, and he did not want to contaminate the crime scene by stepping over the body (and a pool of blood) to reach the basement stairs. Instead, he secured the scene and waited for detectives. Detective Michael Dion arrived on the scene and made a protective sweep of the basement, but no one was there. However, he did find a note dated July 8, 2008, which read, "Ray and Annette Richardson did this."2 The note was written on the back of one of the defendant's pay stubs.

The victim's baseball bat, which usually was kept in the living room closet, was found next to his body and was bloodstained. Blood spatter patterns indicated that he had been beaten. Dr. Andrew Sexton, the medical examiner who performed the autopsy, opined that the cause of the victim's death was "cranial cerebral trauma due to blunt force injuries to the head." Dr. Sexton stated that the victim had sustained five wounds to his head. He opined that a blow to the right side of the victim's forehead had "shatter[ed]" his skull and, by itself, was capable of causing his death. Dr. Sexton further stated that the victim had sustained rib fractures, forearm fractures (indicative of defensive injuries), and contusions on the lower portion of his left leg.

The next morning, at around 7:30 A.M., Chicopee police officers located the defendant in a wooded area near the Connecticut River, approximately one-half mile from Bouchard's house. He was wearing shorts, socks, and sneakers, his skin was cut and scraped, and he was covered with dirt and mud. The officers placed the defendant in handcuffs, conducted a patfrisk for weapons, and then transported him to the detective bureau at the Chicopee police station. After being advised of his Miranda rights, the defendant agreed to speak with Detective Dion and State Trooper Paul DiPietro. The defendant was alert and spoke freely during the two-hour interview, the officers did not have any difficulty understanding him, and he gave appropriate responses to their questions.3 Trooper DiPietro did have to "redirect" the defendant "a couple of times" when he strayed from the topic at hand.

The defendant told Detective Dion and Trooper DiPietro that after the victim said something "wrong" to him, he retrieved the baseball bat and hit the victim from behind as he walked away from the defendant. The victim asked, "Why? Why are you doing this?" when the defendant began to strike him. The defendant recounted that he continued to beat the victim with the bat after he fell to the floor, and that he hit the victim six times. Once the defendant finished giving his statement, he was arrested for murder.

The defendant's sneakers were seized and submitted to the State police crime laboratory for forensic testing. The victim's deoxyribonucleic acid (DNA) profile was the major profile in "very tiny" blood stains on the defendant's right sneaker.4 The defendant told Detective Dion and Trooper DiPietro that he had left a black bag in the woods. State Trooper Ronald Gibbons located the bag and brought it back to the detective bureau. Among the items found therein were a T-shirt with red-brown stains,5 several bottles and cans of beer, a roll of toilet paper, a box of tissues, duct tape, a Ziploc bag containing pennies, a hospital wristband with the defendant's name on it, a bottle opener, cigarettes, a pair of broken eyeglasses, and a blue cellular telephone case. Bouchard identified the cellular telephone case as belonging to the victim. Approximately five days after the victim's death, his sister, Gabrielle Hochrein, found his cellular telephone, broken into two pieces, in the vicinity of the woods where the defendant had been located by the police; she brought it to the police station and turned it over to Detective Dion.

Dr. Howard Lester, a forensic psychologist, testified on behalf of the defense regarding his assessment of the defendant's mental and physical health. He stated that the defendant, who had engaged in sustained alcohol consumption over the course of forty years, was hospitalized in August, 2007, after his landlord found him lying unresponsive in the street. The defendant was suffering from acute kidney failure, exhibiting signs of alcohol withdrawal, and experiencing cognitive deficits. Subsequent neuropsychological testing revealed that the defendant had Korsakoff syndrome, a "brain disease caused by alcohol." According to Dr. Lester, medical personnel determined that the defendant should not return to work, and that he would need ongoing care either "in a facility" or from a family member. Ultimately, the defendant moved into Bouchard's home after he decided that he could not live with his sister because she would not have permitted him to smoke or drink.6 Dr. Lester testified that the defendant's loss of both his own apartment, about which he was "quite bitter," and his job was "significant" because they were the "two main anchors in his life." In addition, the defendant was unhappy about living at Bouchard's house because his room was in an unfinished basement, because the victim frequently "provok[ed]" him by "pull[ing] tricks on him" and by playing music late at night, and because Bouchard "had a capacity for anger and violence."

Dr. Lester further testified that around May 30, 2008, the defendant drove his vehicle into a tree in what the defendant reported was a suicide attempt. He testified that, after being admitted to a hospital, the defendant was diagnosed with "major depressive disorder recurrent, meaning it comes back, and severe, severe depression and also alcohol dependence." According to Dr. Lester, when the defendant was discharged from the hospital, he returned to Bouchard's home where he continued to drink and failed to take prescribed medication or participate in recommended mental health care.

Subsequent to the victim's death on July 8, 2008, Dr. Lester had an opportunity to speak with the defendant about what had occurred. According to Dr. Lester, the defendant was unable to explain why he had attacked the victim, but he did acknowledge that he "had been angry at [the victim] and frustrated with him." When defense counsel asked Dr. Lester whether, based on his assessment of the defendant, he had an opinion "to a reasonable degree of scientific or psychological certainty whether [the defendant] was capable of appreciating the consequences of his actions being extremely atrocious and cruel at the time of the incident," Dr. Lester testified that the defendant "was not capable. His capacity would have been substantially impaired [because of] his anger, his depression, [and] his impaired judgment[, which would have had] a very negative impact on his decision-making ability at the time."

2. Closing argument and jury instructions. During his closing argument, defense counsel summarized the defense theory of the case when he stated:

In his written request for jury instructions, and during the charge conference, defense counsel asked that, with regard to the theory of extreme atrocity or cruelty, the jury be instructed in accordance with Commonwealth v. Urrea, 443 Mass. 530, 535 (2005) (Urrea), and Commonwealth v. Gould, 380 Mass. 672, 686 & n.16 (1980) (Gould), as follows:

The judge stated that, pursuant to Commonwealth v. Oliveira, 445 Mass. 837 (2006) (Oliveira), he was going to instruct the jury on mental impairment in accordance with the Model Jury Instructions on Homicide 61-62 (1999). Before doing that, the judge correctly instructed the jury on the elements of murder in the first degree on theories of deliberate premeditation and extreme atrocity or cruelty, and of murder in the second degree. The judge then proceeded to instruct the jury on mental impairment, stating in relevant part:

At the conclusion of the instructions, defense counsel objected to the fact that the judge did not give defense counsel's requested instruction on mental impairment.

3. Discussion. The defendant's sole defense with regard to the theory of extreme atrocity or cruelty was that his mental impairment rendered him incapable of understanding the consequences of his actions. In the defendant's view, notwithstanding the fact that the judge's instruction on mental impairment conformed with the Model Jury Instructions on Homicide, supra, the instruction was too vague to offer any real guidance to the jurors about the relevance of mental impairment to the analysis of extreme atrocity or cruelty. Relying on Urrea, supra at 535, quoting Gould, supra at 686 & n.16, the defendant asserts that the instruction did not direct the jurors to consider the defendant's capacity to "make a decision in a normal manner" or to evaluate whether his impairment affected his "ability to appreciate the consequences of his choices." Further, the defendant continues, the judge's instruction did not direct the jury to consider the defendant's mental capacity in relation to all of the factors relevant to determining whether the Commonwealth proved extreme atrocity or cruelty. The defendant contends that the judge's refusal to give the requested instruction seriously hindered his ability to present his only defense to the allegations that he committed murder in the first degree with extreme atrocity or cruelty. Accordingly, in the defendant's view, his conviction cannot stand. We disagree.

Where, as here, the judge did not give a requested instruction and, after the judge completed his charge, the defendant objected to the omission of the instruction, we review the judge's action to determine whether there was error and, if so, whether the error prejudiced the defendant. See Commonwealth v. Rogers, 459 Mass. 249, 252-253, cert. denied, 132 S.Ct. 813 (2011); Commonwealth v. Williams, 439 Mass. 678, 682 (2003). Cf. Commonwealth v. Flebotte, 417 Mass. 348, 353 (1994).

To convict a defendant of murder in the first degree on a theory of extreme atrocity or cruelty, the Commonwealth must prove that the defendant committed an unlawful killing with malice aforethought and with extreme atrocity or cruelty. See G. L. c. 265, § 1; G. L. c. 277, § 39. See also Commonwealth v. Auclair, 444 Mass. 348, 361-362 (2005). "Malice is defined in these circumstances as an intent to cause death, to cause grievous bodily harm, or to do an act which, in the circumstances known to the defendant, a reasonable person would have known created a plain and strong likelihood that death would follow." Commonwealth v. Chhim, 447 Mass. 370, 377 (2006). See Commonwealth v. Perry, 432 Mass. 214, 221-222 (2000). It is well established that "[t]he jury are permitted to infer malice from the use of a dangerous weapon." Commonwealth v. Guy, 441 Mass. 96, 107 (2004). See Commonwealth v. Obershaw, 435 Mass. 794, 808-809 (2002); Commonwealth v. Benjamin, 430 Mass. 673, 681 (2000). As discussed infra, a conviction of murder in the first degree on a theory of extreme atrocity or cruelty must be based on evidence of at least one of the factors enunciated in Commonwealth v. Cunneen, 389 Mass. 216, 227 (1983) (Cunneen). See Commonwealth v. Rosenthal, 432 Mass. 124, 129-130 (2000).

In Gould, supra at 684-685, this court indicated for the first time that a defendant's mental impairment could be considered by a jury as evidence bearing on the issue whether the defendant committed murder with extreme atrocity or cruelty. See Commonwealth v. Breese, 389 Mass. 540, 546 (1983) (recognizing that Gould represented "major change in Massachusetts law" and was clear break from past jurisprudence). We explained in Gould, supra at 685-686, that "[t]he jurors' broad discretion will more accurately reflect the community's conscience, goals, and norms, if the jurors are not arbitrarily restricted to considering only the defendant's course of action, but are also permitted to consider the defendant's peculiar mental state as an additional factor to be weighed in determining whether the murder was committed with extreme atrocity or cruelty. Impairment of a defendant's ability to make a decision in a normal manner may have a direct bearing on the degree of murder, and consequently, on the issue of extreme atrocity or cruelty." (Footnote omitted.) See Urrea, supra at 536 (evidence of defendant's mental impairment may mitigate atrocity or cruelty of murder); Commonwealth v. Breese, supra at 549 ("defendant's impaired mind may be considered as one factor among many in determining extreme atrocity or cruelty"). Accordingly, we noted in Gould, supra at 686 n.16, that, "in addition to the traditional instructions on extreme atrocity or cruelty[,] the judge may also instruct the jurors that if they find from the evidence that the defendant had substantially reduced mental capacity at the time the crime was committed, they may consider what effect, if any, the defendant's impaired capacity had on his ability to appreciate the consequences of his choices." The import of this footnote was to confer on judges the discretion to alert jurors to the possibility that a defendant's mental impairment could impact whether murder was committed with extreme atrocity or cruelty. See, e.g., Commonwealth v. Shelley, 381 Mass. 340, 354 (1980) (jury may consider whether, due to mental impairment, defendant "lacked substantial capacity to appreciate the nature of his extremely atrocious or cruel acts, or ... lacked the capacity to stop committing such acts").

At first blush, the language in Gould, supra, regarding a judge's discretion to instruct a jury on a defendant's mental impairment, appeared to suggest that the court was introducing a new mens rea element to the crime of murder in the first degree based on extreme atrocity or cruelty. However, our jurisprudence following Gould clearly has rejected this suggestion. In Cunneen, supra at 226-227, we resolved an issue neither raised nor considered in Gould, namely whether some additional mental element apart from malice aforethought was required to support a conviction of murder in the first degree based on extreme atrocity or cruelty. See Gould, supra at 683 n.14. We adhered to our view that "proof of malice aforethought is the only requisite mental intent" necessary for such a conviction. Cunneen, supra at 227. In other words, there is no requirement that a defendant have a specific mental intent or knowledge of the character of his acts beyond malice aforethought to be convicted of murder in the first degree based on extreme atrocity or cruelty. See id. at 226-227. "This has been our consistent interpretation of G. L. c. 265, § 1, St. 1858, c. 154, since Commonwealth v. Gilbert, 165 Mass. 45, 59 (1895), where this court concluded that under the statute, `[a] murder committed with malice aforethought may be found to have been committed with extreme atrocity or cruelty, even though the murderer did not know that his act was extremely atrocious or cruel.'" Cunneen, supra at 227. See Commonwealth v. Breese, supra at 545-546, and cases cited.

In Cunneen, supra, we articulated a number of factors that a jury can consider in determining whether a murder was committed with extreme atrocity or cruelty, including "indifference to or taking pleasure in the victim's suffering, consciousness and degree of suffering of the victim, extent of physical injuries, number of blows, manner and force with which delivered, instrument employed, and disproportion between the means needed to cause death and those employed." Recognizing that it had diluted to some extent the objective test of whether an act is extremely atrocious or cruel — given that indifference to or pleasure in the victim's pain as well as a defendant's reduced mental capacity are deemed to be relevant considerations — the court in Cunneen unequivocally declined to make the absence of a mental impairment an element of the crime. See Cunneen, supra at 228-229. See also Commonwealth v. Oliveira, supra at 847 (Cunneen confirmed that defendant's mental impairment only "an evidentiary factor that the jury could consider along with other delineated factors" in determining whether murder committed with extreme atrocity or cruelty); Commonwealth v. Rosenthal, supra at 130; Commonwealth v. James, 427 Mass. 312, 316 (1998); Commonwealth v. Breese, supra at 549.

The instruction sought by the defendant here was similar to language set forth in Gould, supra at 686 n.16, that "the judge may also instruct the jurors that if they find from the evidence that the defendant had substantially reduced mental capacity at the time the crime was committed, they may consider what effect, if any, the defendant's impaired capacity had on his ability to appreciate the consequences of his choices." This language in Gould was suggested before our decision in Cunneen, and we subsequently have concluded that "its precise use is not required." Commonwealth v. Oliveira, supra at 848. See Commonwealth v. Painten, 429 Mass. 536, 548 (1999), quoting Gould, supra ("judge was not required to instruct the jury that they could consider whether the defendant's alleged intoxication affected her ability `to appreciate the consequences of [her] choices'"); Commonwealth v. Murphy, 426 Mass. 395, 400 (1998) ("we have never said that the Gould instruction must be repeated verbatim"). Moreover, we have said that "the language in the Model Jury Instructions is consistent with our holding in Commonwealth v. Cunneen, supra [at 228], that while reduced mental capacity is relevant to the jury's exercise of their broad discretion as a reflection of the community's conscience, there is no greater mens rea required for murder by extreme atrocity or cruelty than there is for murder in the second degree, and the crime does not require that the defendant be aware that his acts were extremely cruel or atrocious." Commonwealth v. Oliveira, supra at 848-849.

Here, in explaining the elements of murder in the first degree committed with extreme atrocity or cruelty, the judge directed the jurors to consider each of the Cunneen factors, and he listed them accurately. The judge subsequently instructed the jury in conformity with the Model Jury Instructions on Homicide 61-62 (1999) regarding their consideration of evidence of the defendant's mental impairment. Our jurisprudence does not require that the jury be instructed in the exact words requested by the defendant, see Commonwealth v. Sanders, 451 Mass. 290, 300 (2008), and we see no reason to alter the model jury instructions.

The defendant's reliance on Commonwealth v. Rutkowski, 459 Mass. 794 (2011), to support his contention that the judge erred in failing to give his requested instruction on mental impairment is misplaced. There, the judge instructed the jury on mental impairment only as it related to intent and knowledge, which are not aspects of extreme atrocity or cruelty. See id. at 797-798. We concluded that the judge's failure to instruct the jury "that they could consider evidence of mental impairment on the specific question whether the murder was committed with extreme atrocity or cruelty" constituted error requiring reversal. Id. at 798. Here, by contrast, the judge properly instructed the jury that they could consider evidence of mental impairment in determining whether the defendant acted with extreme atrocity or cruelty in causing the victim's death.

The defendant urges this court to exercise its extraordinary power pursuant to G. L. c. 278, § 33E, to reduce his conviction to murder in the second degree. We have reviewed the entire trial record and conclude that there is no reason to reduce the defendant's murder conviction to a lesser degree of guilt.

Judgment affirmed.