Question

find the maximum or minimum value or the quadratic relation y = x^2 + 8x + 15 

Does the relation have a maximum or minimum value?

Answer 1

Since the coefficient of $x^2$ is positive, then the graph of this quadratic function is parabola with branches upward, which means it has no maximum but has minimum. The minimum of that function is y-coordinate of the vertex. The x-coordinate of the vertex can be found the next way

$x_v=-{\frac b {2a}}$ , where a, b - coefficients of $x^2,x$ respectivelly. So, we have

$x_v=-{\frac 8 2}=-4$

To find y-coordinate we should put x = -4 in the equation, so

$y_x=(-4)^2-8*4+15=-1$

The function has minimum in point (-4;-1)