5. A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.

Question

c) State the equation of the axis of symmetry.

Answer 1

The axis of symmetry is a vertical line that passes through the vertex of the parabola. Its equation is given by:

𝑥 = −𝑏/2𝑎

where 𝑏 is the coefficient of the linear term (−10) and 𝑎 is the coefficient of the quadratic term (1) in the equation 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐.

Substituting these values, we get:

𝑥 = −(−10)/2(1)

𝑥 = 5

Therefore, the equation of the axis of symmetry is 𝑥 = 5.