Question

find the y-intercept of the parabola with the following equation. enter your answer as an ordered pair (x, y).
$f(x) = -10x^2 - 8x + 6$
show your work here

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = f(x)\) occurs where \(x = 0\), since the y - axis is defined by \(x = 0\). So we need to substitute \(x = 0\) into the function \(f(x)=- 10x^{2}-8x + 6\).

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

Substitute \(x = 0\) into \(f(x)\):
\(f(0)=-10(0)^{2}-8(0)+6\)
First, calculate the terms with \(x\): \(-10(0)^{2}=0\) and \(-8(0) = 0\). Then we have \(f(0)=0 - 0+6=6\).

Since when \(x = 0\), \(y=f(0) = 6\), the y - intercept as an ordered pair \((x,y)\) is \((0,6)\).

Answer:

\((0, 6)\)