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2019 MCAS
Grade 10 Mathematics
Question 9 - Score Point 4

Answer for Score Point 4 This question has four parts. A line and a parabola are graphed on a coordinate plane. The equation of the line and the equation of the parabola are shown in this table. This table has two columns labeled Graph and Equation. The first row is Line, y equals negative three x plus five; the second row is Parabola, y equals negative x squared plus two x plus one. Part A What is the value of y for the line when x equals negative four? Show or explain how you got your answer. Enter your answer and your work or explanation in the space provided. The value of y, when x equals negative four is seventeen. I got my answer by just plugging in x equals negative four into the equation. y equals negative three x plus five, y equals negative three times open parenthesis negative four close parenthesis plus five equals seventeen. Part B What is the value of y for the parabola when x equals negative four? Show or explain how you got your answer. Enter your answer and your work or explanation in the space provided. The value of y, when x equals negative four is negative twenty-three. I got my answer by plugging in x equals negative four into the equation y equals negative x squared plus two x plus one equals negative open parenthesis negative four close parenthesis squared plus two times open parenthesis negative four close parenthesis plus one equals negative twenty-three. Part C The line and the parabola intersect at two points. The distance, in units, between the two points is represented by this expression. the square root of open parenthesis four minus one closed parenthesis squared plus open parenthesis negative seven minus two close parenthesis squared Simplify the expression to determine the distance, in units, between the two points. Show or explain how you got your answer. Enter your answer and your work or explanation in the space provided. The distance between the two points is three times the square root of ten. I got my answer by solving the expression above. four minus one equals three, negative seven minus two equals negative nine three squared equals nine, open parenthesis negative nine close parenthesis squared equals eighty-one, nine plus eighty-one equals ninety the square root of ninety equals three times the square root of ten Part D The area, in square units, of the region on the coordinate plane enclosed by the parabola and the line is represented by this expression. negative four cubed over three plus five times four squared over two minus four times four minus open parenthesis negative one cubed over three plus five times one squared over two minus four times one close parenthesis Simplify the expression to determine the area, in square units, of the enclosed region. Show or explain how you got your answer. Enter your answer and your work or explanation in the space provided. The area is four point five. I got my answer by solving t he expression above. negative sixty-four over three plus forty minus sixteen minus open parenthesis negative eleven over six close parenthesis equals four point five.



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Massachusetts Department of Elementary and Secondary Education Print Now | Close Window