Question

algebra 1B CPcomplete the square of the function and identify the maximum or minimum value of the function

Answer 1

Given

`\begin{gathered} y=-2x^2+8x-4 \\ (dy)/(dx)=-4x+8 \\ \text{put it equal to zero.} \\ -4x+8=0 \\ -4x=-8 \\ x=(8)/(4) \\ x=2 \end{gathered}`
`(d^2y)/(dx^2)=-4`

Since, double derivative is negative. So, x=2 gives the point of maxima.

And, the maxima is given as,

`\begin{gathered} y=-2x^2+8x-4 \\ y_(\max )=-2(2)^2+8(2)-4 \\ y_(\max )=-2(4)+16-4 \\ y_(\max )=-8+16-4 \\ y_(\max )=8-4 \\ y_(\max )=4 \end{gathered}`