A parabola intersects the 
\[x\]-axis at 
\[x=3\] and 
\[x=9\].

To describe a parabola that intersects the \( x \)-axis at \( x = 3 \) and \( x = 9 \), we can use the **factored form** of the quadratic equation:

\[
y = a(x - 3)(x - 9)
\]

Here:
- \( x = 3 \) and \( x = 9 \) are the roots (or zeros) of the parabola, meaning the points where the parabola intersects the \( x \)-axis.
- \( a \) is a constant that determines the **vertical stretch** or **compression** of the parabola, as well as whether it opens upwards or downwards. If \( a > 0 \), the parabola opens upwards; if \( a < 0 \), it opens downwards.

To fully define the parabola, you'd need additional information, such as a specific point on the curve or the value of \( a \).

Would you like more details on this? Let me know!

Here are some related questions to explore:
1. How do you find the vertex of a parabola?
2. What happens to the graph if the value of \( a \) changes?
3. How do you calculate the axis of symmetry for this parabola?
4. How would the equation change if the parabola opened downward?
5. Can we determine the maximum or minimum value of the parabola?

**Tip:** The vertex of a parabola that intersects the \( x \)-axis at two points can be found by averaging the \( x \)-coordinates of those points.

A parabola intersects the x-axis at x = 3 and x = 9.

This problem explains how to find the equation of a parabola that intersects the x-axis at x = 3 and x = 9. Explore the factored form of quadratic equations, understand the role of constants, and discover how to calculate the axis of symmetry. 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