Question

Solve the quadratic equation (h - 2)² = 9

using the quadratic formula.
A) h = 5
B) h = -1
C) h = 11
D) h = -5
E) h = 3

Answer 1

To solve the quadratic equation (h - 2)² = 9 using the quadratic formula, rearrange the equation to get it in the form ax² + bx + c = 0. Then, use the quadratic formula to find the values of h. The correct answers are h = 5 and h = -1.

Step-by-step explanation:

To solve the quadratic equation (h - 2)² = 9 using the quadratic formula, we need to rearrange the equation to get it in the form ax² + bx + c = 0. In this case, we have (h - 2)² - 9 = 0. Expanding, we get h² - 4h + 4 - 9 = 0, which simplifies to h² - 4h - 5 = 0. Comparing this with the general quadratic equation ax² + bx + c = 0, we have a = 1, b = -4, and c = -5.

Now, we can use the quadratic formula h = (-b ± √(b² - 4ac)) / (2a) to find the values of h. Plugging in the values, we get:

h = (-(-4) ± √((-4)² - 4(1)(-5))) / (2(1))

h = (4 ± √(16 + 20)) / 2

h = (4 ± √36) / 2

h = (4 ± 6) / 2

Therefore, the solutions to the equation are h = (4 + 6) / 2 = 5 and h = (4 - 6) / 2 = -1. So, the correct answers are A) h = 5 and B) h = -1.