Question

what is the y-intercept of the graph of the function $f(x) = x^2 + 3x + 5$?
$(0, -5)$
$(0, -3)$
$(0, 3)$
$(0, 5)$

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) is the point where the graph intersects the y-axis, which occurs when \( x = 0 \).

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

For the function \( f(x)=x^{2}+3x + 5 \), substitute \( x = 0 \):
\( f(0)=(0)^{2}+3(0)+5 \)

Step3: Simplify the expression

Simplify \( (0)^{2}+3(0)+5 \):
\( 0 + 0+5=5 \)

So, when \( x = 0 \), \( y = 5 \), meaning the y-intercept is \( (0, 5) \).

Answer:

(0, 5)