https://file.aiquickdraw.com/mathbot/file/1727043718321p7q90wn2.jpg

You are asked to graph the function \( f(x) = 2x^2 - 3 \) and plot five points on the graph, including one point with \( x = 0 \), two with negative \( x \)-values, and two with positive \( x \)-values.

To graph this function, let's calculate some points by substituting different values of \( x \) into the function \( f(x) = 2x^2 - 3 \):

### 1. \( x = 0 \):
\[
f(0) = 2(0)^2 - 3 = -3
\]
Point: \( (0, -3) \)

### 2. \( x = -2 \) (negative):
\[
f(-2) = 2(-2)^2 - 3 = 2(4) - 3 = 8 - 3 = 5
\]
Point: \( (-2, 5) \)

### 3. \( x = -1 \) (negative):
\[
f(-1) = 2(-1)^2 - 3 = 2(1) - 3 = 2 - 3 = -1
\]
Point: \( (-1, -1) \)

### 4. \( x = 1 \) (positive):
\[
f(1) = 2(1)^2 - 3 = 2(1) - 3 = 2 - 3 = -1
\]
Point: \( (1, -1) \)

### 5. \( x = 2 \) (positive):
\[
f(2) = 2(2)^2 - 3 = 2(4) - 3 = 8 - 3 = 5
\]
Point: \( (2, 5) \)

### The five points to plot are:
- \( (0, -3) \)
- \( (-2, 5) \)
- \( (-1, -1) \)
- \( (1, -1) \)
- \( (2, 5) \)

You can now use these points to plot the graph on your grid. It will form a parabola opening upwards since the coefficient of \( x^2 \) is positive.

Would you like more details or have any questions?

### 5 Related Questions:
1. How do you determine the vertex of a parabola?
2. What is the axis of symmetry for this parabola?
3. How can you find the intercepts of the graph with the x-axis?
4. How would the graph change if the function were \( f(x) = -2x^2 + 3 \)?
5. What are the steps to find the domain and range of this quadratic function?

### Tip:
When graphing parabolas, always calculate points symmetrically around the vertex to ensure accuracy.

Graph the function f(x) = 2x^2 - 3 and plot five points on the graph, including one point with x = 0, two points with negative x-values, and two points with positive x-values.

Learn how to graph the quadratic function f(x) = 2x^2 - 3 by plotting key points. Understand the properties of parabolas, including the vertex, axis of symmetry, and plotting points with both negative and positive x-values. Suitable for students in 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