Question

find the y-intercept, the axis of symmetry, and the vertex of the graph of the function.\\( f(x) = 3x^2 + 24x + 7 \\)\\( \\)\\( \\)the y-intercept is \\( (0,7) \\). (type an ordered pair.)\\( \\)the axis of symmetry is \\( \square \\). (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 from the function

In the function \( f(x) = 3x^2 + 24x + 7 \), we have \( a = 3 \) and \( b = 24 \).

Step3: Substitute a and b into the formula

Substitute \( a = 3 \) and \( b = 24 \) into \( x = -\frac{b}{2a} \):
\( x = -\frac{24}{2\times3} \)

Step4: Simplify the expression

First, calculate the denominator: \( 2\times3 = 6 \). Then, \( -\frac{24}{6} = -4 \). So the axis of symmetry is \( x = -4 \).

Answer:

\( x = -4 \)