For what value of h is the expression (x-h) ^2+6 equivalent to the expression x^2-6x+15

For what value of h is the expression (x-h) ^2-6 equivalent to the expression x^2-2x-5

1. h=3 2. h=1

Step-by-step explanation:

You need to make both sides into perfect square trinomials that you factor into the perfect square of a binomial. The left side is almost there to start with.

ax² + bx + c is the standard equation

1. (x - h) ² + 6 = x² - 6x + 15 subtract 6 from both sides to get (x - h) ² alone

- 6 - 6

(x - h) ² = x² - 6x + 9 factor the right side into a perfect square (b/2)

here b = - 6 so b/2 = - 3 so (x - 3) ²

(x - 3) ² = (x - 3) (x - 3) = FOIL (first, outside, inside, last)

(x) (x) + (-3) (x) + (-3) (x) + (-3) (-3) = x² - 3x - 3x + 9

= x² - 6x + 9 = (x - 3) ² so

(x - h) ² = (x - 3) ² so h = 3

ax² + bx + c is the standard equation

2. (x - h) ² - 6 = x² - 2x - 5 add 6 to both sides to get (x - h) ² alone

+ 6 + 6

(x - h) ² = x² - 2x + 1 factor the right side into a perfect square (b/2)

here b = - 2 so b/2 = - 1 so (x - 1) ²

(x - 1) ² = (x - 1) (x - 1) = FOIL (first, outside, inside, last)

(x) (x) + (-1) (x) + (-1) (x) + (-1) (-1) = x² - 1x - 1x + 1

= x² - 2x + 1 = (x - 1) ² so

(x - h) ² = (x - 1) ² so h = 1