Question

What is the axis of symmetry of the function f(x) = –(x + 9)(x – 21)?

Answer 1

f(x) = -(x + 9)(x - 21)
= -x² + 12x + 189
Know, f(x) = -x² + 12x + 189 , graph of it is parabolic open vertically downward as shown in figure.
Axis of symmetry is the axis of graph , graph will be symmetrical about it.
for parabola , axis of symmetry is passing through vertex of it.
Find vertex :
Co-ordinate of vertex of parabola ax² + bx + c is given by
(-b/2a , -D/4a)

so, vertex for f(x) = -x² + 12x + 189 is [-2/2(-1), {-(144 + 4 × 189)}/4(-1)}]
= (6 , 225)

so, axis of symmetry will be x = 6