Question

what is the y - intercept of the function?
$f(x)=3x^2 - 4x - 9$
the y - intercept is \\(\square\\). (type an ordered pair, using integers or decimals.)

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 \( f(x)=3x^{2}-4x - 9 \).

Step2: Substitute x = 0 into the function

When \( x = 0 \), we have \( f(0)=3(0)^{2}-4(0)-9 \).
First, calculate \( 3(0)^{2}=3\times0 = 0 \), \( - 4(0)=0 \). Then \( f(0)=0 - 0-9=-9 \).
So the y - intercept is the ordered pair \( (0,-9) \) since when \( x = 0 \), \( y=f(0)=-9 \).

Answer:

\((0, - 9)\)