What is the vertex of -2x2 plus 2x plus 3?

Answer 1

Since this question is in the calculus section, I'm assuming you know how to take the derivative. We know that y = -2x2 + 2x + 3 is a parabola, so it has one vertex, which is a minimum. We can use the first derivative test to find this extreme point.

First, take the derivative:

y' = -4x + 2

Next, set y' equal to zero:

0 = -4x + 2

Then solve for x:

4x = 2

x = 2

This is the x-coordinate of the vertex. To find the y-coordinate, plug x = 2 back into the original equation:

y = -2x2 + 2x + 3

y = -8 + 4 + 3

y = -1

So the vertex is at (2, -1).