Verified answer

y = x^2 + 8x + 13

y = x^2 + 8x + (8/2)^2 + 13 - (8/2)^2

y = (x + 4)^2 + 13 - 16

y = (x + 4)^2 - 3

vertex is (-4, -3)

Complete the square or use the formula -b/2a. I will show both ways.

Completing the square:

y = x² + 8x + 13

y - 13 = x² + 8x

y - 13 + 16 = x² + 8x + 16

y + 3 = (x + 4)²

y = (x + 4)² - 3

This is vertex form: y = a(x - h)² + k where (h, k) is the vertex so the vertex is (-4, -3)

Formula (-b/2a):

The equation is in standard form which is ax² + bx + c.

Here a = 1, b = 8, and c = 13

Use -b/2a

-8/(2)(1)

-8/2 = -4; this is the x-coordinate of the vertex. To find the y-value, substitute the x-value in the original equation: (-4)² + 8(-4) + 13

16 - 32 + 13

29 - 32 = -3

The vertex is (-4, -3). Both ways are useful, but in my opinion the formula is easier to use and less time consuming. It also requires a lot less math.

8X8X8+13

Divided by pie X 100