Label the vertex, the axis of symmetry, and the x and y intercepts of : y=8-2(x-1)squared

Question

show the steps out so i can learn

Answer 1

y = 8-2(x-1)²

Ok so first you want it in the form y = a(x-h)² + k so move the 8 over.

y = -2(x-1)² + 8

Since 'a' (-2) is negative, you know that it opens down. That's just good to know in the future.

The vertex will be (-h,k) so that's (1, 8)

The axis of symmetry is simply the x value of the vertex, so that would be x = 1.

To find the x intercept(s), let y = 0

0 = -2(x-1)² + 8 *move the 8 to the left side

-8 = -2(x-1)² *divide by -2

4 = (x-1)² *square root both sides, taking +/- of the left side

± 2 = x-1 *finally add 1 to both sides

x = 3 and x = -1

To find the y intercept, let x = 0

y = -2(0-1)² + 8

y = -2(1) + 8

y = 6

Hope that helps!