Question

The vertex of the functions graph is given. Find c. y=2x^2-6x+c;(3/2, 0.5)

Answer 1

You would best do this by completing the square on the quadratic and subbing in the vertex they give you, like this:
$2(x- \frac{3}{2})^{2} = \frac{18}{4}-c$
Since the y coordinate of the vertex is 1/2 and we need to solve for c, set the $\frac{18}{4}-c$ equal to 1/2 and solve for c, which is the whole point of what we are doing, right?
$\frac{18}{4}-c= \frac{1}{2}$ and $\frac{18}{4}- \frac{2}{4}=c$
$\frac{16}{4}=c$ and c = 4. So that's our answer!