Given the equation of the parabola (x + 3)^2 = -24(y - 4). What is the value of the x-coordinate of the vertex?

The given equation of the parabola is:

\[
(x + 3)^2 = -24(y - 4)
\]

This equation is in the form \((x - h)^2 = 4p(y - k)\), which represents a parabola that opens either upward or downward. In this standard form:

- \((h, k)\) is the vertex of the parabola.
- \(h\) is the x-coordinate of the vertex.
- \(k\) is the y-coordinate of the vertex.

Comparing the given equation to the standard form, we have:

\[
(x + 3)^2 = -24(y - 4)
\]

Here, \(h = -3\) and \(k = 4\). Therefore, the vertex of the parabola is at \((-3, 4)\).

So, the value of the x-coordinate of the vertex is \( \boxed{-3} \).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you find the y-coordinate of the vertex from the given equation?
2. What is the value of \( p \) in the equation, and how does it relate to the parabola's properties?
3. How would you determine the direction in which the parabola opens?
4. What is the equation of the axis of symmetry for this parabola?
5. How would you find the focus of this parabola?

**Tip:** The sign of the coefficient of \( y - k \) in the equation of a parabola can tell you whether it opens upwards or downwards.

Learn how to find the x-coordinate of the vertex of the parabola (x + 3)^2 = -24(y - 4) using the vertex form of a parabola equation. Understand the relationship between the standard form and the vertex coordinates. Suitable for high school students studying parabolas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation