QuestionPart 4 of 11
For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through (f). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down.
The vertex is $(-3,-9)$ . (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is $x=-3$ . (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? Concave down Concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is $\square$ (Type an integer or a simplified fraction.) B. There is no $y$ -intercept.

Studdy Solution
To find the $x$ -intercepts, solve the equation $f(x) = 0$ .
$x^2 + 6x = 0$
Factor the quadratic equation:
$x(x + 6) = 0$
Set each factor equal to zero:
$x = 0 \quad \text{or} \quad x + 6 = 0$
Solve for $x$ :
$x = 0 \quad \text{or} \quad x = -6$
The $x$ -intercepts are $(0, 0)$ and $(-6, 0)$ .
The $y$ -intercept is:
$\boxed{(0, 0)}$
The $x$ -intercepts are:
$\boxed{(0, 0)} \quad \text{and} \quad \boxed{(-6, 0)}$

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