Home > INT3 > Chapter 7 > Lesson 7.1.2 > Problem7-30

7-30.

A parabola has vertex $\left(2, 3\right)$ and contains the point $\left(0, 0\right)$. Write an equation for this parabola. Homework Help ✎

For a vertically-oriented parabola, use the equation $y = a\left(x − h\right)^{2} + k$ where $\left(h, k\right) = \left(2, 3\right)$ and $\left(x, y\right) = \left(0, 0\right)$.
For a "sleeping parabola" use the equation $x = a\left(y − k\right)^{2} + h$.

$0 = a\left(0 − 2\right)^{2} + 3$

$−3 = a\left(4\right)$

$-\frac{3}{4}=a$

$y=-\frac{3}{4}(x-2)^2+3$