Question

Write a quadratic function to model the graph to the right.
Question content area bottom left
Part 1
​f(x)equals
  
enter your response here
.
.
.
Question content area right
Part 1
-10
-8
-6
-4
-2
2
4
6
8
10
-4
-2
2
4
6
8
10
12
14
16
18
20
x
y

Answer 1

To model a quadratic function, we typically need either the vertex form, the standard form, or we can also find the roots if we have the x-intercepts.

Since you mentioned that there is a graph to the right, but I cannot see it, I will outline how to derive a quadratic function based on common characteristics of a parabola.

### Vertex Form
A commonly used form is the vertex form of a quadratic function which is expressed as:

\[
f(x) = a(x - h)^2 + k
\]

where:
- \( (h, k) \) is the vertex of the parabola.
- \( a \) determines the direction of the parabola (if \( a > 0 \), it opens upwards; if \( a < 0 \), it opens downwards).

### Steps to Follow
1. **Identify the Vertex**:
If you have the coordinates of the vertex from the graph, you can replace \( h \) and \( k \) with those values.

2. **Identify a Point**:
If there is another point on the graph (other than the vertex), use its coordinates \( (x_1, y_1) \) to solve for \( a \).

3. **Write the Equation**:
Substitute \( h \), \( k \), and \( a \) back into the vertex form equation.

### Example
Let’s say the vertex from the graph is at (2, 3) and you have a point on the graph at (0, 0). You would:

1. Start with the vertex:
\[ f(x) = a(x - 2)^2 + 3 \]

2. Substitute the point (0, 0):
\[ 0 = a(0 - 2)^2 + 3 \]
\[ 0 = 4a + 3 \]
\[ 4a = -3 \]
\[ a = -\frac{3}{4} \]

3. Write the final equation:
\[ f(x) = -\frac{3}{4}(x - 2)^2 + 3 \]

If you have specific coordinates from the graph, I can help you find the exact quadratic function!