Question

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

Answer 1

Answer:

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