Question

what is the y intercept of f(x)=-x2+12x-32

Answer 1

what is the vertex

Answer 2

To find the y-intercept of a function, you need to set x = 0 and solve for y.

Given the function f(x) = -x^2 + 12x - 32,
Substituting x = 0, we get:
f(0) = -(0^2) + 12(0) - 32
= -32

Therefore, the y-intercept of f(x) = -x^2 + 12x - 32 is -32.

Answer 3

To find the vertex of a quadratic function in the form f(x) = ax^2 + bx + c, you can use the formula:

x = -b / (2a)

For the function f(x) = -x^2 + 12x - 32, we can identify a = -1, b = 12, and c = -32.

Using the formula, we can calculate the x-coordinate of the vertex:
x = -12 / (2*(-1))
x = -12 / -2
x = 6

To find the y-coordinate of the vertex, we substitute the x-coordinate into the original function:
f(6) = -(6^2) + 12(6) - 32
= -36 + 72 - 32
= 4

Therefore, the vertex of the function f(x) = -x^2 + 12x - 32 is (6, 4).