Question

a quadratic function f(x) is hidden from view. you must find the y-intercept(s) of f(x) and write the answer(s) in the form (x, y). choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently.
form: vertex form f(x) = 2(x + 1)^2 - 50
answer attempt 1 out of 2
there are no y-intercepts
there are no y-intercepts
there is one y-intercept
there are two y-intercepts

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) is the point where \( x = 0 \), so we substitute \( x = 0 \) into the function.

Step2: Substitute \( x = 0 \) into \( f(x)=2(x + 1)^2-50 \)

First, calculate \( (0 + 1)^2=1^2 = 1 \). Then, \( 2\times1=2 \). Finally, \( f(0)=2 - 50=-48 \). So the y - intercept is at \( (0,-48) \), which means there is one y - intercept.

Answer:

There is one y - intercept, and the y - intercept is \( (0, - 48) \)