### Home > A2C > Chapter 4 > Lesson 4.2.4 > Problem4-119

4-119.

A parabola has vertex $\left(2, 3\right)$ and contains the point $\left(0, 0\right)$.

1. If this parabola is a function, find its equation.

Use the equation$y = a\left(x − h\right)^{2} + k$; if $\left(h, k\right) = \left(2, 3\right)$; at $(0, 0)$.

$0 = a\left(0 − 2\right)^{2} + 3$

$−3 = a\left(4\right)$

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

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

2. Suppose this parabola is not a function, but is a “sleeping” parabola. Find its equation.

Use the equation $x = b\left(y − k\right)^{2} + h$; if $\left(h, k\right) = \left(2, 3\right)$; at $\left(0, 0\right)$.

Use the eTool below to graph the equations.
Click the link at right for the full version of the eTool: A2C 4-119 HW eTool