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2019 MCAS
Grade 10 Mathematics
Question 9 - Score Point 2

Answer for Score Point 2 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 open parenthesis sixteen close parenthesis minus eight plus one y equals negative sixteen minus seven 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 open parenthesis open parenthesis four minus one close parenthesis squared plus open parenthesis negative seven minus two close parenthesis squared close parenthesis the square root of open parenthesis open parenthesis three squared close parenthesis minus nine squared close parenthesis the square root of nine minus eighty-one the square root of seventy-two eight 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 four cubed over three plus five times four squared over two minus four times four plus open parenthesis one cubed over three plus five times one squared over two minus four times one close parenthesis negative fifty-four over three plus five times sixteen over two minus sixteen plus open parenthesis one over three plus five over two minus four close parenthesis negative fifty-four over three plus seventy over two minus sixteen plus open parenthesis two over six plus fifteen over six minus four close parenthesis negative eighteen plus thirty-five minus sixteen plus open parenthesis seventeen over six minus four close parenthesis seventeen minus sixteen plus open parenthesis seventeen over six minus twenty-four over six close parenthesis one plus open parenthesis seven over six close parenthesis six over six plus seven over six thirteen over six



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