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
