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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. y equals negative three open parenthesis negative four close parenthesis plus five y equals twelve plus five y 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. y equals negative open parenthesis negative four close parenthesis squared plus two open parenthesis negative four close parenthesis plus one y equals negative sixteen minus eight plus one y 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 square root of three squared plus open parenthesis negative nine close parenthesis squared the square root of nine plus eighty-one 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. negative sixty-four over three plus eighty over two minus sixteen minus open parenthesis negative one over three plus five over two minus four close parenthesis negative sixty-four over three plus forty minus sixteen minus open parenthesis negative two over six plus fifteen over six minus twenty-four over six close parenthesis negative one hundred twenty-eight over six plus two hundred forty over six minus ninety-six over six minus open parenthesis negativ eleven over 6 close parenthesis negative one hundred twenty-eight over six plus two hundred forty over six minus ninety-six over six plus eleven over six twenty-seven over six equals four and one half



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