Posted by **CC** on Tuesday, June 7, 2011 at 10:47pm.

13. Find the vertex of the parabola.

y = -2x2 + 12x - 13

(5, -3)

(-3, 5)

(3, 5)

(5, 3)

- Math -
**Jai**, Tuesday, June 7, 2011 at 11:03pm
y = -2x^2 + 12x - 13

there are many ways to determine the vertex, but the easiest (for me) i think is to use derivatives. first we get the derivative with respect to x:

y = -2x^2 + 12x - 13

y' = -4x + 12

then we equate this to zero (because vertex is a maximum or a minimum and therefore the slope is zero):

0 = -4x + 12

4x = 12

x = 3

substitute this back to the original given equation:

y = -2x^2 + 12x - 13

y = -2(3^2) + 12(3) - 13

y = -18 + 36 - 13

y = 5

therefore vertex is at

(3, 5)

hope this helps~ :)

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