Mathematics

Problem

For the quadratic function

f(x)=ax^{2}+bx+c

, where

a\neq 0

, answer the following: a. (i) Derive an expression for the

x

–coordinate of the vertex in terms of

a

and

b

. Hence write the equation of the axis of symmetry. b. (ii) Show algebraically that every point

(x_1,y_1)

on the graph has a mirror image across the axis of symmetry, and identify the mirror image of the point

(p,q)

. c. (iii) Explain how the sign of

a

decides whether the vertex gives the maximum or the minimum value of the function.