Question

Given f(x)= x^2+7x+8, find x when f(x)= -4.
My answer is -4.

Find x if f(x)=0 and f(x)= 6x^2-7x-3.
My answer is -3.

Find the equation of the axis of symmetry of f(x)=x^2-12x+17.
I have no idea how to figure this problem.

Answer 1

yes, -4 works but it is a parabola, two solutions
x^2 +7 x +8 = -4
x^2 + 7 x +12 = 0
(x+4)(x+3) = 0
x = -4 or x = -3

No, I did (2x-3)(3x+1) = 0
x = 3/2 or x = -1/3

y = x^2 -12 x +17
x^2 - 12 x = y-17
complete the square to look for symmetry
x^2 -12 x + 36 = y -17 +36
(x-6)^2 = y + 19
symmetry about x = 6
for example if x =8
(x-6)^2 = 2^2 = 4
and if x = 4, on the other side of x = 6 then
(x-6)^2 = (-2)^2 = 4 ,the same

Answer 2

The axis of symmetry is a straight line which runs through the vertex of a parabola, cutting in in "half", and becoming a line of reflection.

Find the vertex by whatever method you learned, for your case you should get (6,-19)
then the equation of the axis of symmetry would be
x = 6