Question

The graph of a parabola is given. Match graph to its equation.

and equations of the parabola are$$\begin{gathered} A)y^2=4xC)y^2=-4xE){(y-1)}^2=4(x-1)G){(y-1)}^2=-4(x-1) \\ B)x^2=4yD)x^2=-4yF){(x+1)}^2=4(y+1)H){(x+1)}^2=4(y+1) \end{gathered}$$

Short answer

Given graph represent the graph of${(x+1)}^2=4(y+1)$.

Step-by-step solution

Step 1. Given information.

We have given graph is

and equations of the parabola are

Step 2. Concept used.

General equation of the parabola is,${\left(x-h\right)}^2=4a\left(y-k\right)\hspace{0.17em}and\hspace{0.17em}{\left(y-k\right)}^2=4a\left(x-h\right)$

Step 3. Explanation.

We have graph of the parabola is,

This graph is opens down and vertex of the parabola is (-1, -1).

Graph is opens downward so a is negative (a < 0).

This graph represent the equation${(x+1)}^2=4(y+1)$

Step 4. Conclusion.

Hence, equation of the graph

is${(x+1)}^2=4(y+1)$.