Question

which of the following is the y-intercept of $g(x) = -2(x + 3)^2 - 7$?

a $(0, -18)$

b $(0, -25)$

c $(0, 9)$

d $(0, -11)$

e $(0, -7)$

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = g(x)\) is the point where \(x = 0\). So we need to substitute \(x = 0\) into the function \(g(x)=-2(x + 3)^{2}-7\).

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

First, calculate \((0 + 3)^{2}\). Since \(0+3 = 3\), then \((0 + 3)^{2}=3^{2}=9\).

Then, multiply this result by \(- 2\): \(-2\times9=-18\).

Next, subtract 7 from the above result: \(-18-7=-25\).

So when \(x = 0\), \(g(0)=-25\), which means the y - intercept is \((0,-25)\).

Answer:

B. (0, -25)