Question

what is the vertex of -2x^2+4x-10

Answer 1

Would you like to Complete the Square or just drop it out of the sky?

Answer 2

You have here a parabola in the form \[y =ax^2+bx+c\]The x-value of the vertex of such a parabola is always given by \[x = -\frac{b}{2a}\]You can plug in the values of \(a\) and \(b\) (determined by comparing your equation with mine) and get the \(x\) value at the vertex. Then evaluate the equation at that value of \(x\) to find the corresponding \(y\) value.

Completing the square works by giving you the equation of the parabola in vertex form: \[y = (x-h)^2+k\]where the vertex is located at \((h,k)\)

You could also solve for the roots of the equation (values of \(x\) where \(y = 0\)) with the quadratic formula or graphing or whatever. A parabola has symmetry about the vertex, so a line from the vertex perpendicular to the x-axis will intercept the x-axis exactly midway between those two roots. If you know the roots, just take their average and you've got the \(x\) value of the vertex, then plug it into the equation to find the \(y\) value. If you happen to get a quadratic with roots having an imaginary component, the real component of the roots is located at the \(x\) value of the vertex (the parabola won't cross the x-axis if the roots aren't real).

Answer 3

Well, then it appears you have entered the equation incorrectly. Please give it a better try.

-b/(2a) = -4/(2*(-2)) = 1

The vertex is at x = 1.

Keep graphing until it is.