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2019 MCAS
Grade 10 Mathematics
Question 9 - Score Point 3

Answer for Score Point 3 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 x plus five. Substitute negative four in for x and solve. y equals negative three open parenthesis negative four close parenthesis plus five. Simplify. 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 x squared plus two x plus one. Substitute negative four in for x and solve. 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 open parenthesis three close parenthesis squared plus open parenthesis negative nine close parenthesis squared. the square root of nine plus eighty-one. the square root of ninety. 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 open parenthesis sixty-four over three close parenthesis plus eighty over two minus sixteen. negative open parenthesis one hundred twenty-eight over six close parenthesis plus two hundred forty over six minus ninety-six over six equals sixteen over six sixteen over six minus open parenthesis negative two over six plus fifteen over six minus twenty-four over six close parenthesis sixteen over six minus open parenthesis negative thirty-seven over six close parenthesis equals five hundred ninety-two over six open parenthesis units close parenthesis squared.



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