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2019 MCAS
Grade 10 Mathematics
Question 9 - Score Point 1

Answer for Score Point 1 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 this by plugging in the negative four into the equation so the new equation for the line is y equals negtive three open parenthesis negative four close parenthesis plus five. this simplifies out to y equals seventeen so therefore the value is 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 the parabola is nine. I got this by plugging the negative four into all the x values. When you do that the equation you get is y equals negative open parenthesis negative four close parenthesis squared plus two open parenthesis negative four close parenthesis plus one. This simplifies out to nine which is the value of the parabola. 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 points is ten. I know this because when you simplify the equation you get the square root of open parenthesis nine close parenthesis plus open parenthesis eighty-one close parenthesis then that simplifies to the square root of one hundred which equals 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 of the region is negative four hundred eighteen over three. I got this by simplifying the equation into negative sixty-four over three plus one hundred two over three open parenthesis negative two over six plus fifteen over six minus twenty-four over six close parenthesis. This then simplified to seventy-six over six open parenthesis negative eleven over six close parenthesis when you multiply those two together you get negative four hundred eighteen over three.



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