Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).

f(x) = –2(x − 4)2 + 2

g(x) = 5x2 − 10x + 7

Answer 1

if we have a generic parabola:
\[\Large y = a{x^2} + bx + c\]
then its simmetry axis, is given by the subsequent equation:
\[\Large x = - \frac{b}{{2a}}\]

Answer 2

for example, for g(x), we have the subsequent coefficients:
a=5,
b=-10
c=7, so the equation of the symmetry axis, is:
\[\Large x = - \frac{b}{{2a}} = - \frac{{ - 10}}{{2 \times 5}} = ...?\]

Answer 3

what is:
\[ \Large - \frac{{ - 10}}{{2 \times 5}} = ...?\]