 The parabola opens in what direction given the equation       y^2 =  -16x  



The given equation is:

\[
y^2 = -16x
\]

This equation is in the form \(y^2 = 4px\), which represents a parabola that opens either to the right or to the left.

- If \(4p > 0\), the parabola opens to the right.
- If \(4p < 0\), the parabola opens to the left.

In your equation, \(4p = -16\), so:

\[
p = \frac{-16}{4} = -4
\]

Since \(p\) is negative, the parabola opens to the **left**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What is the vertex of the parabola given by the equation \(y^2 = -16x\)?
2. How would you find the focus of this parabola?
3. What is the directrix of the parabola \(y^2 = -16x\)?
4. How would the graph change if the equation were \(y^2 = 16x\)?
5. How can you determine the length of the latus rectum for this parabola?

**Tip:** For a parabola in the form \(y^2 = 4px\), the focus is at \((p, 0)\) and the directrix is the line \(x = -p\).

Explore the direction of a parabola given the equation y^2 = -16x. Understand how to determine the direction based on the coefficient p in the standard form y^2 = 4px. This problem involves analyzing parabolic curves and is suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation