Name:

WEST SPRING SECONDARY SCHOOL

"THIRST FOR KNOWLEDGE"

( ) Class; Date:

WORKSHEET 18

Chapter.?: Graphs of Functions

Sketching of Quadratic Functions (X-intercept Form)

Previously we learned we can express quadratic functions in the form of y = (x- nf + k or y - -(x-h) + k,then sketch the graph.

Today, we learn another form, the x-intercept form, in which quadratic functions can be expressed.They are:

or ^

Graphs of y = ±(x - p\x - q)

We can change the Quadratic Function from y = ax2 + bx + cto the form y = ±(x - pfc - q) byFactorisation.

-> To sketch the graph of y = ±(x - /?X* - <?)

We need to know these important information.(1) Upward Shaping (+x2) vj or- Downward Shaping (-x ) n(2) x - intercept : by substituting y = 0 into the equation

- > x = p or x = q

(3) y - intercept : by substituting x = 0 into the equation

(4) The equation of the Line of Symmetry, x = —

(5) Turning Point:

Minimum Point or Maximum Point occurs when x = *—-=-

Graph of y = (x- pfo - q) Graph of y = ~(x-

O

o

EXAMPLE 1

Sketch the graph of y = x2 + 3x - 4 .

J- ( x - I )( x -f 4

©V

EXAMPLE 2

Sketch the graph of y - -x2 + 3x - 2

x -

.2

= -C4 -oci

EXAMPLE 3

Sketch the graph of y - 5x- x

X - O or X -

X = O

O,_(A) jL*r± tf. / X -

'n.4

w r

EXAMPLE 4i— -^

Sketch the graph of _y ~ -x2 - 2jc - 1 .

0

y r -

= 2

S/

a P-j"

2.

' I

x = -

= O

B-J.I.-*- "

EXAMPLE 5

Sketch the graph of y = (x + \](x - 4).

©V 1

-o

EXAMPLE 6The curve y = ax2 + bx + c crosses the axes at A (-3, 0), B (6, 0) and C.(a) Find the values of a, b and c.(b) Hence, state the coordinates of C.(c) The point (5, h) lies on the curve. Find the value of h.

O)-6*1- 3

A\ O

=^ , J=C-

B

EXAMPLE 7

The diagram shows the graph of y = x2 + ax + b. The graph cuts the x-axis at (2,0rand (6,0). It cuts they-axis at C.(a) Calculate the values of a and b,(b) Write down the coordinates of C.(c) Write down the equation of the line of symmetry of the

graph.

3"- X X —

O

- iz-C ^/

X --r -^.

HOMEWORK

1 .

(a)

(b)

(c)

Sketch the graphs for the following quadratic equations, showing clearly:• x-intercept• y-intercept• line of symmetry (state the equation)• max/min point (state the coordinates)

- -2

^ -2.

x -* +- / t-A^- M

o- 2.

U c

u j. t; 0-4-9

=^%c-g

X =

.'

2.

®/*\i w =

Jj -

hi2-

-i ^ - -Z./ W - -

/ _ -I J

4.

A graph of y - (x + 2)(6 - x) cuts the y-axis at A and the x-axis at B and C(a) Find the coordinates of A,(b) Find the coordinates of B and C,(c) The equation of the line of symmetry(d) Sketch the graph, showing clearly all of the above. r t^ $

x,-a*i* , J-0

^ -2A.

The sketch represents the graph of the parabola y - -,x2 + fex + c . Find(a) the values of b and c(b) the coordinates of the turning point of the parabola.

V-^

. ; J i =

**$- (2

The diagram below shows the graph ofthe coordinates of(a) A, (b) B, (c) C

= (x - 2)(x + 5). Points A, B and C lie on the curve. Find

fit J

Answers:2a)A(0 , 12)4a) (-5, 0)

2b) B (-2,0); C{6,0) 2c) x=24b)(2,0) 4c)(0, 10)

3a) b=7, c= 3b) (3.5, 12.25)