Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function.
$f(x) = 5x^2 + 5x + 11$
the y - intercept is $(0,11)$. (type an ordered pair.)
the axis of symmetry is \boxed{}. (simplify your answer. type an equation.)

Explanation:

Step1: Recall axis of symmetry formula

For a quadratic function \( f(x) = ax^2 + bx + c \), the axis of symmetry is given by the formula \( x = -\frac{b}{2a} \).

Step2: Identify \( a \) and \( b \)

In the function \( f(x) = 5x^2 + 5x + 11 \), we have \( a = 5 \) and \( b = 5 \).

Step3: Substitute into the formula

Substitute \( a = 5 \) and \( b = 5 \) into the formula \( x = -\frac{b}{2a} \):
\[
x = -\frac{5}{2 \times 5}
\]

Step4: Simplify the expression

Simplify the right - hand side:
\[
x = -\frac{5}{10}=-\frac{1}{2}
\]

Answer:

The axis of symmetry is \( x = -\frac{1}{2} \)