What is the relative minimum of the function ?

Minimum of the function is -2.

Step-by-step explanation:

For any parabola which is in the form of y= +a(x-h)²+k

If the equation starts with positive notation then parabola will be  like figure shown in the question and this parabola will have minimum value of the function.

And if the function starts with negative notation y=-a(x-h)²+k then parabola will have maximum.

Now the minimum value of the function is the y coordinate of its vertex means if vertex is (h, k) then k will be the minimum of the function.

Now from the figure of parabola vertex is (-3, -2).

So minimum of the parabola is "y coordinate of vertex" that is -2.

a king of hearts and a 2 of spades

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.