Quadratic Functions
Graphs
● Factorising quadratic expression gives information about the graph of the
function
● X-intercepts found from numbers in each bracket
● Y-intercept is product of numbers in brackets
● If there is a single negative x in the factorised expression, the graph is
inverted
Example
S ketch the curve y = x2 + 5x + 6
x2 + 5x + 6 = (x + 2)(x + 3)
x − intercepts at x =− 2 and x =− 3
y − intercept at y = 6
Disguised Quadratics
● Some graphs don’t look like quadratics
● Can be rewritten as conventional-looking quadratics
Example
S olve x4 − x2 − 6 = 0
Let y = x2
y2 − y − 6 = 0
(y − 3)(y + 2) = 0
y = 3, y = − 2 → x2 = 3, x2 = − 2
x = ± √3
Graphs
● Factorising quadratic expression gives information about the graph of the
function
● X-intercepts found from numbers in each bracket
● Y-intercept is product of numbers in brackets
● If there is a single negative x in the factorised expression, the graph is
inverted
Example
S ketch the curve y = x2 + 5x + 6
x2 + 5x + 6 = (x + 2)(x + 3)
x − intercepts at x =− 2 and x =− 3
y − intercept at y = 6
Disguised Quadratics
● Some graphs don’t look like quadratics
● Can be rewritten as conventional-looking quadratics
Example
S olve x4 − x2 − 6 = 0
Let y = x2
y2 − y − 6 = 0
(y − 3)(y + 2) = 0
y = 3, y = − 2 → x2 = 3, x2 = − 2
x = ± √3
