Question

3
select the correct answer.
what is the y-intercept of this quadratic function?
f(x) = x² + 2x + 3
a. (0,-3)
b. (0,1)
c. (0,3)
d. (0,-1)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function is the point where \(x = 0\) (since it's the intersection with the y - axis, where the x - coordinate is 0). So we need to find \(f(0)\) for the function \(f(x)=x^{2}+2x + 3\).

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

Substitute \(x = 0\) into \(f(x)=x^{2}+2x + 3\). We get \(f(0)=(0)^{2}+2\times(0)+3\).
Simplify the expression: \((0)^{2}=0\), \(2\times(0) = 0\), so \(f(0)=0 + 0+3=3\).
So the y - intercept is the point \((0,3)\) because when \(x = 0\), \(y=f(0) = 3\).

Answer:

C. \((0,3)\)