Graph the function f(x)=
–
7x2.
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the firs

To graph the function \( f(x) = -7x^2 \), we need to follow these steps:

### Step 1: Identify the Vertex
The given function is a quadratic in the form of \( f(x) = ax^2 + bx + c \). In this case:
- \( a = -7 \)
- \( b = 0 \)
- \( c = 0 \)

The vertex of a parabola in this form is at the point \( (h, k) \), where:
- \( h = \frac{-b}{2a} = 0 \)
- \( k = f(h) = f(0) = 0 \)

So, the vertex is at \( (0, 0) \).

### Step 2: Plot the Vertex
Plot the vertex at the point \( (0, 0) \) on the graph.

### Step 3: Plot Another Point
Choose another value for \( x \) to find a second point on the parabola. For example, let's use \( x = 1 \):
- \( f(1) = -7(1)^2 = -7 \)
So, the point \( (1, -7) \) is another point on the parabola.

### Step 4: Plot the Point and Draw the Parabola
Now plot the point \( (1, -7) \) on the graph. Since the parabola is symmetric, you can also plot the point \( (-1, -7) \) on the other side of the vertex.

### Final Step: Draw the Parabola
Draw a smooth curve through the points \( (0, 0) \), \( (1, -7) \), and \( (-1, -7) \). The parabola opens downward because the coefficient of \( x^2 \) is negative.

Would you like further details or have any questions? 

Here are some additional questions related to this topic:
1. What is the axis of symmetry of the parabola?
2. How would the graph change if the coefficient of \( x^2 \) were positive?
3. What are the x-intercepts of the function?
4. How would the graph change if a constant term \( c \) were added to the function?
5. What effect does changing the value of \( a \) (e.g., from -7 to -2) have on the shape of the parabola?

**Tip:** A parabola always opens upward if \( a > 0 \) and downward if \( a < 0 \).

Graph the function f(x) = -7x^2. Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Learn how to graph the quadratic function f(x) = -7x^2. This step-by-step guide explains how to find and plot the vertex, choose additional points, and draw the parabola. Key concepts include graphing parabolas and understanding the impact of negative coefficients on the shape of the graph. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation