Question

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

Answer 1

1. h=3 2. h=1

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