A quadratic function

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

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

, with

a\neq 0

, is given. (i) Define the terms “vertex” and “axis of symmetry” of the parabola represented by

y=g(x)

. (ii) Show algebraically that the

x

-coordinate of the vertex is

-\dfrac{b}{2a}

. (iii) Using the result of (ii), explain whether

g(x)

attains a maximum or a minimum value at the vertex when

a>0

and when

a<0