Question

What did I do wrong? Need help with this equation

Answer 1

Solve the system

$\begin{bmatrix}y=4x-8 \\ y=2\mleft(x-3\mright)^2-2\end{bmatrix}$

Subtract the equations

$\begin{gathered} y-y=4x-8-\mleft(2\mleft(x-3\mright)^2-2\mright) \\ 0=4x-8-2(x-3)^2+2 \\ 0=4x-8-2(x^2-6x+9)+2 \\ 0=4x-8-2x^2+12x-18+2 \\ 0=16x-24-2x^2 \\ 0=-2x^2+16x-24 \end{gathered}$

Solve quadratic equation

$\begin{gathered} 0=-2(x^2-8x+12) \\ 0=-2(x-2)x-6) \end{gathered}$

Then, the solutions are:

$\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \\ \text{For y} \\ y=4(2)-8=8-8=0 \end{gathered}$

And

$\begin{gathered} x-6=0 \\ x-6+6=0+6 \\ x=6 \\ \text{For y } \\ y=4(6)-8=24-8=16 \end{gathered}$

Answer:

(2,0)

(6,16)