Final answer:
The x-intercept of the function is -8, and the y-intercept is 64.
Step-by-step explanation:
The x-intercepts of a quadratic function can be found by setting the function equal to zero and solving for x. In this case, the function is f(x) = x² + 16x + 64. To find the x-intercepts, we set f(x) = 0 and solve the quadratic equation.
x² + 16x + 64 = 0
Using the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), we can find the values of x.
For this equation, a = 1, b = 16, and c = 64.
Substituting the values into the formula, we get:
x = (-16 ± √(16² - 4(1)(64))) / (2(1))
Simplifying further:
x = (-16 ± √(256 - 256)) / 2
x = (-16 ± √0) / 2
x = -16 / 2
x = -8
Therefore, the x-intercept of the function is -8.
In terms of the y-intercept, we substitute x = 0 into the function:
f(0) = (0)² + 16(0) + 64
f(0) = 64
So, the y-intercept of the function is 64.