Question

For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6.

Answer 1

we have that

y = -2x² + 2x +2

Group terms and move the constant to the opposite side of the equation

y -2 = -2x² + 2x

Factor the leading coefficient

y -2 = -2(x²-x )

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

y -2 -0.25*2= -2(x²-x+0.25 )

y -2.50= -2(x²-x+0.25 )

Rewrite as perfect squares

y -2.50= -2(x-0.50)²

Part a) The equation of a parabola in vertex form is. y=a(x−h)2+k

so

y -2.50= -2(x-0.50)²--------> y = -2(x-0.50)²+2.50

the answer Part a) is

y = -2(x-0.50)²+2.50

part b) Find the vertex

we know that the vertex is the point (h,k)

so

(h,k) is the point---------> (0.50,2.50)

the answer part b) is

the vertex is the point (0.50,2.50)

Part c) find the value for x = 6

y = -2(x-0.50)²+2.50-----> y = -2(6-0.50)²+2.50----> y = -2(5.50)²+2.50

y=-60.50+2.50-------> y=-58

the answer Part c) is

-58