Question

Use the graph to determine a. the function's domain; b. the function's range, c. the x-intercepts, if any, d.the y-intercept, if any; and e. the missing function values, indicated by question marks, below.

f(-4)= ?

Answer 1

The function's features are as follow

The domain of parabolic equation is all real numbers

Range: y ≤ 1

c. the x-intercepts: -1 and 1

d. the y-intercept: 1

e f(-4) = -15

How to find the missing value

The missing value of the function is solved by finding the equation of the function

The equation of the function in vertex form is

y = a (x - h)² + k

The vertex is at (0, 1)

y = ax² + 1

Solving for a using point (2, -3)

-3 = a(2)² + 1

-4 = 4a

a = -1

hence the equation is y = -x² + 1

For x = -4

y = -(-4)² + 1 = -15