so is x squared - 3 narrower or wider than y = x squared + c

The equation \( y = x^2 - 3 \) can be compared with \( y = x^2 + c \) to determine if it is narrower or wider.

### Breaking Down the Comparison
- The equation \( y = x^2 - 3 \) has the general form \( y = ax^2 + bx + c \), where:
  - \( a = 1 \) (the coefficient of \( x^2 \))
  - \( b = 0 \)
  - \( c = -3 \)

- The equation \( y = x^2 + c \) also has:
  - \( a = 1 \)
  - \( b = 0 \)
  - \( c = c \) (a constant)

### Coefficient Comparison
In both equations, the coefficient \( a = 1 \), meaning the shape of the parabolas (in terms of width) is the same.

- **Conclusion**: The parabola represented by \( y = x^2 - 3 \) has the same width as the parabola represented by \( y = x^2 + c \), regardless of the value of \( c \). Both are equally wide.

The difference in the equations affects only the vertical position (shift) of the parabola, not its width.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How does changing the value of \( c \) in \( y = x^2 + c \) affect the graph?
2. What is the vertex of the equation \( y = x^2 - 3 \)?
3. How do you determine the axis of symmetry in a quadratic equation?
4. How can you find the roots of the equation \( y = x^2 - 3 \)?
5. What is the effect of changing the sign of \( a \) in a quadratic equation?

**Tip:** When comparing the widths of quadratic functions, focus on the coefficient of \( x^2 \). The constant term only affects the vertical translation of the graph.

Understand the width comparison between parabolas represented by equations x^2 - 3 and x^2 + c. Learn how the coefficient of x^2 affects the shape and width of parabolas in quadratic equations. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation