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### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Finding the Equation of a ParabolaFind an equation of the parabola whose graph is shown

The equation of parabola is ${y}^{2}=x$

See the step by step solution

## Step 1. Given information

Graph of parabola is given as-

## Step 2. Concept used

The equation of a parabola having a vertex at origin is –

${y}^{2}=4px$

Where, $p>0$ then parabola opens to the right

$p<0$ then parabola opens to the left.

The directrix is the right side of $y$-axis is so, which means the focus should be negative, the parabola opens to the left and the coordinates of focus are obtained. On substituting the value of $p$ in the equation ${y}^{2}=4px$ to obtain an equation of a parabola.

## Step 3. Calculation

Substituting the point $\left(4,-2\right)$ in the equation of parabola ${y}^{2}=4px$, we get –

${\left(-2\right)}^{2}=4p\left(4\right)$

$\begin{array}{l}⇒4=16p\\ ⇒16p=4\\ ⇒p=\frac{4}{16}\\ ⇒p=\frac{1}{4}\end{array}$

Now, substituting the value of $p$ in equation ${y}^{2}=4px$ , we get the equation as.

$\begin{array}{l}{y}^{2}=4\left(\frac{1}{4}\right)x\\ ⇒{y}^{2}=x\end{array}$