quadratic graphs 2

7/27/2019 Quadratic Graphs 2

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Quadratic Equations

Different types of Quadratic graph and how

to interpret them



Quadratic Equations

-4 -3 -2 -1 0 1 2 3 4

y = x2

y = x2

+ 3

y = - x2

y = 6 x2

+ 3 moves the curve up the y axis by 3 – the same effect

as with linear equations

6 x2 – the coefficient of x2

makes the parabola narrower

If the coefficient was less than

1, for example 1

2

then the parabola would be

wider

- x2 – a negative coefficient of x2

turns the parabola upside down



Quadratic Equations

Finding solutionsFind the solutions for 2 x2 - 4=0

If we think about the equation:

y = 2 x2

-4We are looking for the values of x such that y = 0

i.e.

0 = 2 x2

- 4 or2 x2 – 4 = 0 because equals means ‘is the same’

we can write it either way

y = 0

is also the equation for the horizontal line through the

origin of the axes



Quadratic Equations

Plot the line y = 2 x2 - 4 and the line y = 0 on a graph

-4 - 3 - 2 - 1 0 1 2 3 4

50

45

40

35

30

25

20

15

10

5

-5

-10

y = 2x 2

- 4

y = 0

The coordinates where the linescross are (-1.4,0) and (1.4,0)

So when y = 0

x = -1.4

and x = 1.4

These are the solutions to:

2 x2 - 4=0

There are usually 2 solutions

to quadratic equations because

of the shape of the graph



Quadratic Equations

-4 - 3 - 2 - 1 0 1 2 3 4

50

45

40

35

30

25

20

15

10

5

-5

-10

y = 2x 2

- 4

y = 10

The coordinates where the linescross are approximately

(-2.6,10) and (2.6,10)

So when y = 10

x =-

2.6and x = 2.6

This can be repeated to find the

solution of 2 x2

- 4 = 10

Draw the lines y = 2 x2 - 4

and y = 10



1. y = x2

2. y = x2 + 5

4. y = - x2 - 5

3. y = 4 x2 + 7

Match the letter of the

graph with the number

of the equation

Worksheet 1 Answers

A

Quadratic Equations

C

B

D1. B

2. D

3. C4. A



AQA Module 5 Foundation p263 Answer Sheet

Quadratic Equations

1. 2.

Worksheet 2 - Answers

= x2 - 4 x

x -1 0 1 2 3 4 5

y 5 0 -3 -4 -3 0 5

= x2 + 2 x + 1

x -4 -3 -2 -1 0 1 2

y 9 4 1 0 1 4 9




3. 4.

Worksheet 3 - Answers

= x2 - 3 x

x -1 0 1 2 3 4 5

y 4 0 -2 -2 0 4 10

Quadratic Equations

= 5 + x - x2

x -3 -2 -1 0 0.5 1 2 3 4

y -7 -1 3 5 5.25 5 3 -1 -7



-4 -3 -2 -1 0 1 2 3 4

1. y = x2

2. y = x2 + 5

4. y = - x2 - 3

3. y = 4 x2

Match the letter of the

graph with the number

of the equation

Worksheet 1

A

Quadratic Equations

C

B

D




Quadratic Equations

1.= x2 - 4 x

x -1 0 1 2 3 4 5

y 5 -4 -3

2.

= x2

+ 2 x + 1

x -4 -3 -2 -1 0 1 2

y 9 1 0 4

Worksheet 2




Quadratic Equations

3. 4.

= x2 - 3 x

x -1 0 1 2 3 4 5

y -2 4

= 5 + x - x2

x -3 -2 -1 0 0.5 1 2 3 4

y -7 5.25 3 -7

Worksheet 3

quadratic graphs 2

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