Question

Determine the amount of and type of solutions of y=-x^2+8x-13

Answer 1

Given:

`y=-x^2+8x-13`

To determine the amount and type of solutions, apply the quadratic formula below:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Replace 0 with y and solve for x.

Where:

a= -1

b= 8

c = -13

Thus, we have:

`0=-x^2+8x-13`

`\begin{gathered} x=\frac{-8\pm\sqrt[]{8^2-4(-1)(-13)}}{2(-1)} \\ \\ x=\frac{-8\pm\sqrt[]{64-52}}{2(-1)} \\ \\ x=\frac{-8\pm\sqrt[]{12}}{-2} \\ \\ x=\frac{-8\pm\sqrt[]{4\ast3}}{-2} \\ \\ x=\frac{-8\pm\sqrt[]{2^2\ast3}}{-2} \end{gathered}`

Solving further:

`\begin{gathered} x=\frac{-8\pm2\sqrt[]{3}}{-2} \\ \\ x=4\pm2\sqrt[]{3} \\ \\ \\ x=4+2\sqrt[]{3},\text{ and 4-2}\sqrt[]{3} \end{gathered}`

ANSWER:

`x=4\pm2\sqrt[]{3}`