Question

graphing quadratic functions
graph this function: ( f(x) = x^2 - 4x - 5 )
step 3: plot the vertex.
step 4: factor the function to find the ( x )-intercepts.
the ( x )-intercepts are: ( (5, 0) ) and ( (-1, 0) )
step 5: plot the ( x )-intercepts.
step 6: find the ( y )-intercept.
( f(0) = -5 )
step 7: plot the ( y )-intercept.

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is the value of the function when \(x = 0\). So we substitute \(x = 0\) into the function \(f(x)=x^{2}-4x - 5\).

Step2: Substitute \(x = 0\) into the function

When \(x = 0\), we have \(f(0)=(0)^{2}-4\times(0)-5\).
First, calculate \((0)^{2}=0\) and \(4\times(0) = 0\). Then \(f(0)=0 - 0-5=- 5\).

Answer:

\(-5\)