Question

In the following exercises, match each graph to one of the following equations:

$$\begin{gathered} a)x^2+y^2=64 \\ b)x^2+y^2=49 \\ c){\left(x+5\right)}^2+{\left(y+2\right)}^2=4 \\ d){\left(x-2\right)}^2+{\left(y-3\right)}^2=9 \\ e)y=-x^2+8x-15 \\ f)y=6x^2+2x-1 \end{gathered}$$

Short answer

The equation of the given graph is$f)y=6x^2+2x-1$

Step-by-step solution

Step 1. Given Information

Given graph is

Given equations to match are:

$$\begin{gathered} a)x^2+y^2=64 \\ b)x^2+y^2=49 \\ c){\left(x+5\right)}^2+{\left(y+2\right)}^2=4 \\ d){\left(x-2\right)}^2+{\left(y-3\right)}^2=9 \\ e)y=-x^2+8x-15 \\ f)y=6x^2+2x-1 \end{gathered}$$

The equation of the given graph among the given equations is to be determined.

Step 2. Equation of the graph

Given graph is an upward opening parabola.

The standard form of an upward opening parabola is $y=a{x}^2+bx+c$where a is positive.

Among the given options, the only equation where a is positive is$y=6x^2+2x-1$

Step 3. Conclusion

The equation of the given graph is$f)y=6x^2+2x-1$