Solve y = X^2+8X-3 and find min/max

Y = x^2 + 8x - 3

The function does not factor so to find the solutions you would have to use the quadratic formula or complete the square.

x^2 + 8x = 3

8/2 = 4

4^2 = 16

add 16 to both sides

x^2 + 8x + 16 = 3 + 16

(x + 4) ^2 = 19

Take the square root of both sides.

x + 4 = + - √19

x = - 4 + - √19 Solutions

Min/Max

Since the leading coefficient is a positive 1, the function will have a minimum value. To find the min, we find the vertex using the formula x = - b/2a

x = - 8/2 = - 4

Now plug - 4 back in to the equation and solve for y.

x^2 + 8x - 3 = y

(-4) ^2 + 8 (-4) - 3 = y

16 - 32 - 3 = y

-19 = y

Vertex (-4, - 19)

The minimum value is - 19 when x = - 4