The parabola y=-2x^ (2) + 8x-c has its vertex at (2,5). What is the value of c?

c = 3

Step-by-step explanation:

The parabola y=-2x^ (2) + 8x-c has its vertex at (2,5). What is the value of c?

we know the vertex ... then the vertex form looks like:

y = a * (x - 2) ^2 + 5

expanded out we get:

a (xx - 4x + 4) + 5 = axx - 4ax + 4a + 5

compare that to y=-2x^ (2) + 8x-c

axx - 4ax + 4a + 5 = - 2x^ (2) + 8x-c

solve ...

axx = - 2xx, a = - 2

then - c = 4a + 5

-c = 4*-2 + 5 = - 8 + 5 = - 3

c = 3