Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function.\\(f(x) = 5x^2 + 5x + 18\\)\
the y - intercept is \\((0,18)\\). (type an ordered pair.)\
the axis of symmetry is \\(x = \\). (simplify your answer. type an equation.)

Explanation:

Step1: Recall the formula for the axis of symmetry of a quadratic function

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

Step2: Identify the values of \( a \) and \( b \) from the given function

In the function \( f(x) = 5x^2 + 5x + 18 \), we have \( a = 5 \) and \( b = 5 \).

Step3: Substitute the values of \( a \) and \( b \) into the formula for the axis of symmetry

Substituting \( a = 5 \) and \( b = 5 \) into \( x = -\frac{b}{2a} \), we get:
\[
x = -\frac{5}{2 \times 5}
\]

Step4: Simplify the expression

Simplifying \( -\frac{5}{2 \times 5} \), the 5 in the numerator and the 5 in the denominator cancel out, leaving:
\[
x = -\frac{1}{2}
\]

Answer:

\( x = -\frac{1}{2} \)