Question

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

Answer 1

c = 3

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