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

The correct match is (D).

Step-by-step solution

Step 1. Given information.

We have given graph is,

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

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 given graph is,

This graph is opens down and vertex of the graph is (0, 0) and point on the graph is

(-2, -1).

Using standard equation of the parabola,

$$\begin{gathered} {(x-h)}^2=4a(y-k) \\ \Rightarrow {(x-0)}^2=4a(y-0) \\ \Rightarrow x^2=4ay \end{gathered}$$

Using the point, (-2, -1)

localid="1646817023642" $$\begin{gathered} 4=-4a \\ \Rightarrow a=-1 \\ \Rightarrow x^2=-4y \end{gathered}$$

Step 4. Conclusion.

Hence, equation of the graph

is$x^2=-4y$