What is the focus of the parabola y = -2x^2 + 4? Simplify any fractions. (______,______)

Write Vertex Form: Write the equation in vertex form. y = -2x^2 + 4 can be written as y = -2(x - 0)^2 + 4, where the vertex (h, k) is (0, 4).Find Value of p: Find the value of p using the formula p = 1/(4a). Here, a = -2, so p = 1/(4*(-2)) = -1/8.Determine Focus: Determine the focus using the vertex and the value of p. Since the parabola opens downwards, the focus is at (h, k + p). So, the focus is at (0, 4 - 1/8) = (0, 31/8).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the focus of the parabola $y = -2x^2 + 4$ ? $\newline$ Simplify any fractions. $\newline$ (,)

View step-by-step help

Home

Math Problems

Algebra 2

Find the focus or directrix of a parabola

Full solution

Q. What is the focus of the parabola

y = -2x^2 + 4

\newline

Simplify any fractions.

\newline

(______,______)

Write Vertex Form: Write the equation in vertex form. $\newline$ $y = -2x^2 + 4$ can be written as $y = -2(x - 0)^2 + 4$ , where the vertex $(h, k)$ is $(0, 4)$ .
Find Value of p: Find the value of $p$ using the formula $p = \frac{1}{4a}$ . Here, $a = -2$ , so $p = \frac{1}{4*(-2)} = -\frac{1}{8}$ .
Determine Focus: Determine the focus using the vertex and the value of $p$ . $\newline$ Since the parabola opens downwards, the focus is at $(h, k + p)$ . $\newline$ So, the focus is at $(0, 4 - \frac{1}{8}) = (0, \frac{31}{8})$ .