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$e)y=-x^2+8x-15$

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 a downward opening parabola.

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

Among the given options, the only equation where a is negative is$y=-x^2+8x-15$

Step 3. Conclusion

The equation of the given graph is$e)y=-x^2+8x-15$