What is the vertex to -5x2 plus 20x-13?

Answer 1

-5x2 + 20x - 13 describes a parabola, and you can find it's vertex in various ways. To find it using calculus, you can simply take it's derivative and solve for 0:

f(x) = -5x2 + 20x - 13

f'(x) = -10x + 20

Let f'(x) = 0, then:

0 = -10x + 20

x = 2

Then simply plug the x value into the original equation:

f(x) = -5 * 22 + 20 * 2 - 13

= -20 + 40 - 13

= 7

So the vertex of this parabola is at the point (2, 7).

To solve it using strictly algebra, you can do it by expressing it as a value of y, and then rearranging accordingly:

y = -5x2 + 20x - 13

y = -5(x2 - 4x) - 13

y = -5(x2 - 4x + 4 - 4) - 13

y = -5(x2 - 4x + 4) + 20 - 13

y = -5(x - 2)2 + 7

From which we can see that the vertex happens at the point (2, 7)