Question

graph (f(x) = x^2 + 8x + 15) below by first selecting the correct shape, clicking the vertex, then clicking an (x)-intercept.

Explanation:

⚡ Using what you learned: graphing quadratic functions

Step 1: Find the vertex

The x-coordinate of the vertex is given by:

$$ x = -\frac{b}{2a} $$

For \( f(x) = x^2 + 8x + 15 \), we have \( a = 1 \) and \( b = 8 \):

$$ x = -\frac{8}{2(1)} = -4 $$

Find the y-coordinate by evaluating \( f(-4) \):

$$ f(-4) = (-4)^2 + 8(-4) + 15 $$

$$ f(-4) = 16 - 32 + 15 = -1 $$

The vertex is at \( (-4, -1) \).

Step 2: Find the x-intercepts

Set \( f(x) = 0 \):

$$ x^2 + 8x + 15 = 0 $$

$$ (x + 3)(x + 5) = 0 $$

$$ x = -3 \quad \text{or} \quad x = -5 $$

The x-intercepts are at \( (-3, 0) \) and \( (-5, 0) \).

Answer:

1. Shape: Select the parabola (U-shape) opening upwards.
2. Vertex: Click on \( (-4, -1) \).
3. x-intercept: Click on either \( (-3, 0) \) or \( (-5, 0) \).