Question

Find the values of x when f(x) = 0. Then, find the y-intercept and vertex point if exists. Sketch the graph of the functions (label the x-intercept, y-intercept and vertex point in the graph).

(a) f(x) = -x + 16
(b) f(x) = 35 - 9x - 2x2

Answer 1

To find the values of x when f(x) = 0, we set the equation equal to 0 and solve for x. For f(x) = -x + 16, x = 16. The y-intercept is 16. The vertex point does not exist for this linear function.

Step-by-step explanation:

To find the values of x when f(x) = 0, we need to set the equation equal to 0 and solve for x. For the equation f(x) = -x + 16, we have:

-x + 16 = 0

Adding x to both sides:

16 = x

So the value of x when f(x) = 0 is 16.

The y-intercept is the value of y when x = 0. Substituting x = 0 into the equation f(x) = -x + 16, we get:

f(0) = -(0) + 16

f(0) = 16

Therefore, the y-intercept is 16.

The vertex point of a linear function is half way between the x-intercepts. Since the equation f(x) = -x + 16 is a linear function with only one x-intercept, the vertex point does not exist.