Chapter 11.4, Problem 17E

To determine

To find: an equation for the conic

Answer to Problem 17E

The equation is $x^2=-\frac{1}{4}\left(y-4\right)$

Explanation of Solution

Given information: The graph provided in the question shown below

  

Calculation: General equation of vertical parabola

  $\begin{array}{l}{\left(x-h\right)}^2=4p\left(y-k\right)\\ vertex:\left(h,k\right)=\left(0,4\right)\\ {\left(x\right)}^2=4p\left(y-4\right)\\ \text{it passes through}\left(1,0\right)\\ {\left(1\right)}^2=4p\left(0-4\right)\\ {\left(1\right)}^2=4p\left(1-4\right)\\ 4p=-\frac{1}{4}\\ p=-\frac{1}{16}\end{array}$

So, the final equation is $x^2=-\frac{1}{4}\left(y-4\right)$