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
