Chapter 11.4, Problem 12E

To determine

To find: the vertex, focus and the directrix of the parabola and sketch the graph

Answer to Problem 12E

The Vertex $=\left(\frac{1}{2},0\right)$ , Focus $=\left(\frac{9}{2},0\right)$ , Directrix $=-\frac{7}{2}$

Explanation of Solution

Given information: The question is

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

Calculation: for the vertex, focus and the directrix of the parabola

Let,

  $\begin{array}{l}{y}^2=16x-8\\ \Rightarrow y^2=16\left(x-\frac{1}{2}\right)\\ y^2=4ax\\ a=4\end{array}$

So,

Vertex $=\left(\frac{1}{2},0\right)$

Focus $=\left(\frac{9}{2},0\right)$

Directrix $=-\frac{7}{2}$