Hi Solveit :))
The function g is defined as g(x)=ax^2+bx-6a, where a and b are positive constants. The function has a line of symmetry at x=-3. Which of the following could NOT be a coordinate pair on the graph of y=g(x)?
A) (0,-3)
B) (0,3)
C) (-3,0)
D) (3,3)
E) (-3,-3)
\(y=ax^2+bx-6a\)
\(\frac{-b}{2a}=-3\\ -b=2a*-3\\ -b=-6a\\ b=6a\\ \mbox{so the equation becomes}\\ y=ax^2+6ax-6a\\ y=a(x^2+6x-6) \)
If x=0 then
y=a(-6) <0 so (0,3) CANNOT be a point but (0,-3) could be
If x=-3
y=a(9-18-6) <0 so (-3,0) CANNOT be a point but (-3,-3) could be
If x=+3
y=a(9+18-6)>0 so (3,3) can be a point
SO
(0,3) and (-3,0) cannot be points on the parabola.