Question

What are the vertex and x-intercepts of the
graph of y = (x + 4)(x - 2)? Select one answer
for the vertex and one for the x-intercepts.
• Vertex: (1, 9)
O x-intercepts: (4, 0), (-2, 0)
• x-intercepts: (-4, 0), (-2, 0)
O x-intercepts: (-4, 0), (2, 0)
• Vertex: (-1, -9)
• Vertex: (-1, -5)

Answer 1

To find the vertex and x-intercepts of the quadratic function \( y = (x + 4)(x - 2) \), we can first expand it into standard form.

### Step 1: Expand the quadratic
\[
y = (x + 4)(x - 2) = x^2 - 2x + 4x - 8 = x^2 + 2x - 8
\]

### Step 2: Find the x-intercepts
To find the x-intercepts, set \( y = 0 \):
\[
0 = x^2 + 2x - 8
\]
Now, we can factor or use the quadratic formula. Factoring gives:
\[
0 = (x + 4)(x - 2)
\]
Setting each factor to zero:
1. \( x + 4 = 0 \) → \( x = -4 \)
2. \( x - 2 = 0 \) → \( x = 2 \)

So the x-intercepts are:
\[
(-4, 0) \text{ and } (2, 0)
\]

### Step 3: Find the vertex
The vertex of a quadratic in the form \( y = ax^2 + bx + c \) can be found using the vertex formula:
\[
x = -\frac{b}{2a}
\]
Here, \( a = 1 \) and \( b = 2 \):
\[
x = -\frac{2}{2(1)} = -1
\]

Now substitute \( x = -1 \) back into the quadratic to find the y-coordinate of the vertex:
\[
y = (-1)^2 + 2(-1) - 8 = 1 - 2 - 8 = -9
\]

Thus, the vertex is:
\[
(-1, -9)
\]

### Summary
- Vertex: \( (-1, -9) \)
- x-intercepts: \( (-4, 0) \) and \( (2, 0) \)

From your options:
- Vertex: **(-1, -9)**
- x-intercepts: **(-4, 0), (2, 0)**

So, you can select:
- **Vertex: (-1, -9)**
- **x-intercepts: (-4, 0), (2, 0)** (not listed correctly, but these would be the x-intercepts)