Question

Graphs of Parabolas Match the equation with the

graphs labeled I–VI. Give reasons for your answers.

$y^2=8x$

Short answer

The graph of parabola $y^2=8x$is

Step-by-step solution

Step 1. Given information.

The given equation of a parabola $y^2=8x$.

Step 2. Write the concept.

The given equation of a parabola $y^2=8x$

Simplifying it further,

$y^2-4\left(2\right)x$

Comparing this with standard equation of the parabola $y^2=4px$, we get the value of p as $2$. Since p > 0, it opens right.

This leaves us with $3^{rd}$ and $6^{th}$graph.

Comparing the other question which has the same graph as this question, we see that $y^2-8x$ has a value of p that is away from the origin causing the mouth of its parabola to be bigger.

This leaves us with the $6^{th}$ graph.

The focus and directrix of the parabola is given by $\left(2,0\right)$ and x = $-2$.