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Chapter 11: Problem 23

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola symmetric about the \(y\) -axis that passes through the point (2,-6)

Short Answer

Expert verified
Answer: The equation of the parabola is \(y = - \frac{3}{2}x^2\).

Step by step solution

01

Identify given information

We are given the following information: - Vertex of the parabola is at the origin: (0, 0) - The parabola is symmetric about the y-axis - The parabola passes through the point (2, -6)
02

Determine the general form of the equation

Since the parabola is symmetric about the y-axis, its equation will take the form of: \(y = ax^2\) Our goal is to find the value of 'a'.
03

Use the given point to find 'a'

The parabola passes through the point (2, -6). Substitute the coordinates of this point into the general equation, and solve for 'a': \(-6 = a(2^2)\) \(-6 = 4a\) Now, divide both sides by 4 to get the value of 'a': \(a = - \frac{6}{4}\) \(a = - \frac{3}{2}\)
04

Write the equation of the parabola

Now that we have found the value of 'a', we can write the equation of the parabola: \(y = - \frac{3}{2}x^2\) So, the equation of the parabola with the given conditions is \(y = - \frac{3}{2}x^2\).

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Most popular questions from this chapter

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