Question

what is the y-intercept of the function?\\( f(x) = 3x^2 - 2x - 7 \\)\
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 \( y = f(x) \) is the point where \( x = 0 \), so we substitute \( x = 0 \) into the function.

Step2: Substitute \( x = 0 \) into \( f(x) \)

For the function \( f(x)=3x^{2}-2x - 7 \), when \( x = 0 \), we have \( f(0)=3(0)^{2}-2(0)-7 \).
Simplify the expression: \( 3\times0 - 0 - 7=-7 \).
So the y - intercept is the ordered pair \( (0, - 7) \).

Answer:

\((0, -7)\)