Question

Given the table of values, complete the table for the quadratic equation y=−6x2+3x+8 𝑦 = − 6 𝑥 2 + 3 𝑥 + 8 to find the values of the high or low point of the parabola. This table shows the corresponding values of x and y, with some missing values for y. Steps Solution x y −1 − 1 −1 − 1 −0.75 − 0.75 2.375 −0.5 − 0.5 5 −0.25 − 0.25 0 8 0.25 8.375 0.5 0.75 1 5 Which of the following is correct? (1 point) Responses (0.25,8.375) ( 0.25 , 8.375 ) is the high point on the parabola. left parenthesis 0.25 comma 8.375 right parenthesis is the high point on the parabola. (−1,−1) ( − 1 , − 1 ) is the low point on the parabola. left parenthesis negative 1 comma negative 1 right parenthesis is the low point on the parabola. (0.25,8.375) ( 0.25 , 8.375 ) is the low point on the parabola. left parenthesis 0.25 comma 8.375 right parenthesis is the low point on the parabola. (0.5,9) ( 0.5 , 9 ) is the high point on the parabola.

Answer 1

First find the vertex: x = −b/(2a) = −3/(2·(−6)) = 0.25.
Plug in: y = −6(0.25)^2 + 3(0.25) + 8 = −0.375 + 0.75 + 8 = 8.375.

Since a = −6 < 0 the parabola opens downward, so the vertex is a maximum. Answer: (0.25, 8.375) is the high point.