Chapter 9.3, Problem 16WE

To determine

To find: The equation of the parabola.

Answer to Problem 16WE

The required equation of the parabola is $y-1=\frac{1}{4}{\left(x+3\right)}^2$ .

Explanation of Solution

Given information: It is given, focus $\left(-2,1\right)$ and vertex $\left(-3,1\right)$ .

Formula used: $y=\frac{1}{4c}{\left(x-h\right)}^2+k$

Calculation: Since vertex is below the focus, so it open upwards.

Here, $\left(h,k\right)=\left(-3,1\right)$

The distance from the vertex to the focus is $\frac{1}{4c}$ .

Since it opens upward we use positive C.

  $\begin{array}{l}\frac{1}{4c}=\frac{1}{4\times 1}\\ =\frac{1}{4}\end{array}$

Now, put the value of $\left(h,k\right)$ into the standard equation.

  $\begin{array}{l}y=\frac{1}{4}{\left(x-\left(-3\right)\right)}^2+1\\ y-1=\frac{1}{4}{\left(x+3\right)}^2\end{array}$

Now, graph the parabola,