Cambridge International Mathematics

Given the equation of any curve:

Anx-interceptis a value ofxwhere the graph meets the

x-axis.

x-intercepts are found by lettingybe 0 in the equation

of the curve.

Ay-interceptis a value ofywhere the graph meets the

y-axis.

y-intercepts are found by lettingxbe 0 in the equation

of the curve.

Discovery 2 Axes intercepts

What to do:

1 For the following functions, use a graphing package or graphics calculator to:

i draw the graph ii find they-intercept iii find anyx-intercepts.

a y=x^2 ¡ 3 x¡ 4 b y=¡x^2 +2x+8 c y=2x^2 ¡ 3 x

d y=¡ 2 x^2 +2x¡ 3 e y=(x¡1)(x¡3) f y=¡(x+ 2)(x¡3)

g y=3(x+ 1)(x+4) h y=2(x¡2)^2 i y=¡3(x+1)^2

2 From your observations in question 1 :

a State they-intercept of a quadratic function in the form y=ax^2 +bx+c.

b State thex-intercepts of quadratic function in the form y=a(x¡®)(x¡ ̄).

c What do you notice about thex-intercepts of quadratic functions in the form y=a(x¡®)^2?

THEy-INTERCEPT

You will have noticed that for a quadratic function of the form y=ax^2 +bx+c, they-intercept is the

constant termc. This is because any curve cuts they-axis whenx=0.

For example, if y=x^2 ¡ 2 x¡ 3 and we let x=0

then y=0^2 ¡2(0)¡ 3

) y=¡ 3 (the constant term)

THEx-INTERCEPTS

You should have noticed that for a quadratic function of the form y=a(x¡®)(x¡ ̄), thex-intercepts

are®and ̄. This is because any curve cuts thex-axis when y=0.

So, if we substitute y=0 into the function we get a(x¡®)(x¡ ̄)=0

) x=®or ̄ fby the Null Factor lawg

This suggests thatx-intercepts are easy to find when the quadratic is infactorisedform.

F AXES INTERCEPTS [3.2]

x

y

these points

are -interceptsx

the

y-intercept

O

GRAPHING

PACKAGE

438 Quadratic equations and functions (Chapter 21)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\438IGCSE01_21.CDR Monday, 27 October 2008 2:09:41 PM PETER