Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

Graph the equation: $y+4=x^2$

Step-by-Step Solution

Answer

The graph of $y+4=x^2$is

Step 1. Give data

The given equation is

$y+4=x^2$

Step 2. Properties of equation

Rearrange the equation into the standard form of the equation of the parabola 

$$\begin{gathered} y+4=x^2 \\ {x}^2=y+4 \\ {\left(x-0\right)}^2=4\left(\frac{1}{4}\right)\left[y-\left(-4\right)\right] \\ {\left(x-h\right)}^2=4p(y-k) \end{gathered}$$

So vertex of parabola is $(h,k)=(0,-4)$

and focus is $(h,k+p)=0,-3.75)$

Step 3. Graph

Plot a parabola of the vertex$(0,-4)$ to plot the graph of $y+4=x^2$