Final answer:
To find solutions where h(x) equals g(x), set the g(x) function equal to the constant value of h(x) and solve for x. The resulting quadratic equation is then solved using the quadratic formula to find the solutions to the nearest hundredth.
Step-by-step explanation:
The student needs to find the solutions for when h(x) equals g(x). Since h(x) is given as a constant function with the value 5, we simply set g(x) equal to 5 to find the x-values that make the two functions equal.
The equation for g(x) is given: g(x) = -x² + 2x + 12. To find the solutions, we set g(x) = 5.
The equation becomes:
-x² + 2x + 12 = 5
Simplify to:
-x² + 2x + 7 = 0
This is a quadratic equation, and it can be solved using the quadratic formula:
x = ∛[-b ± (b² - 4ac)]/(2a)
In this equation, a = -1, b = 2, and c = 7. Plugging these values into the quadratic formula we can solve for x and find the solutions to the nearest hundredth.