Question

For the given quadratic equation convert into vertex form, find the vertex and find the value for x=6 Y=-2x^2+2x+2

Answer 1

Answer:

Part 1) The vertex is the point (0.50,2.50)

part 2) $y=-58$

Step-by-step explanation:

we have

$y=-2x^{2} +2x+2$

Part 1) Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-2=-2x^{2} +2x$

Factor the leading coefficient

$y-2=-2(x^{2} -x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-2-0.50=-2(x^{2} -x+0.25)$

$y-2.50=-2(x^{2} -x+0.25)$

$y-2.50=-2(x-0.50)^{2}$

$y=-2(x-0.50)^{2}+2.50$ -----> equation in vertex form

The vertex is the point (0.50,2.50)

Part 2) Find the value of y for x=6

substitute the value of x in the equation

$y=-2(6)^{2} +2(6)+2$

$y=-72 +12+2$

$y=-58$