Question

for the quadratic function f(x)=-x^{2}-2x, answer parts (a) through (f). (type an integer or a simplified fraction.)

b. there is no y - intercept.

what is the x - intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the x - intercept(s) is/are
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. there is/are no x - intercept(s).

Explanation:

Step1: Find the y - intercept

Set \(x = 0\) in \(f(x)=-x^{2}-2x\). Then \(f(0)=-(0)^{2}-2(0)=0\).

Step2: Find the x - intercept

Set \(y = f(x)=0\), so \(-x^{2}-2x = 0\). Factor out \(-x\): \(-x(x + 2)=0\).

Step3: Solve for x

Using the zero - product property, if \(-x(x + 2)=0\), then \(-x=0\) or \(x + 2=0\). Solving \(-x=0\) gives \(x = 0\), and solving \(x+2=0\) gives \(x=-2\).

Answer:

The y - intercept is \(0\).
A. The x - intercept(s) is/are \(0,-2\)