Question

use the quadratic function ( f(x)=\frac{1}{4}x^2 + 4x + 6 ) to answer the following questions.
a) use the vertex formula to determine the vertex.
the vertex is ( (-8, -10) ). (type an ordered pair. simplify your answer.)
b) does the graph \open up\ or \open down\?

c) what is the equation of the axis of symmetry?
( x = -8 ) (simplify your answer.)
d) find the y - intercept. select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the y - intercept is (type an integer or a fraction.)
b. there is no y - intercept.

Explanation:

Part d)

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) is the value of \( f(x) \) when \( x = 0 \). So we substitute \( x = 0 \) into the function \( f(x)=\frac{1}{4}x^{2}+4x + 6 \).

Step2: Substitute \( x = 0 \)

\( f(0)=\frac{1}{4}(0)^{2}+4(0)+6 \)

Step3: Simplify the expression

\( \frac{1}{4}(0)=0 \), \( 4(0)=0 \), so \( f(0)=0 + 0+6=6 \).

Answer:

The y - intercept is \( 6 \)