Question

the graphs of the function with equation y= a(x+5)^2=q passes through the points (-6,2) and (-3,20).
Determine whether the function has a maximum or minimum value

Answer 1

I will assume you mean
y= a(x+5)^2 + q , ( + and = are on the same key)
for the point (-6,2) ,
2 = a(-1)^2 + q ---> a + q = 2
for the point (-3,20) ,
20 = a(4) + q ---> 4a + q = 20

solve these two equations, I suggest subtracting them

Answer 2

THis is a really nice question : )
If you sub one of the points into the equation (for x and y) you obtain equation 1 in values of q and a.
If you then sub the second point (-3, 20) into the original equation
20 = a(- 3 + 5)^2 + q you obtain equation 2.
When you use equations 1 and 2 and "subtract" them, you can find the value of "a". If "a" equals a positive number then the quadratic opens upwards (and is a minimum), if "a" equals a negative number then the quadratic opens downwards (and is a minimum) : )