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7/27/2019 Quadratic Graphs 2
http://slidepdf.com/reader/full/quadratic-graphs-2 1/11
Quadratic Equations
Different types of Quadratic graph and how
to interpret them
7/27/2019 Quadratic Graphs 2
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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
7/27/2019 Quadratic Graphs 2
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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
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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
7/27/2019 Quadratic Graphs 2
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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
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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
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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
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AQA Module 5 Foundation p263 Answer Sheet
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
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-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
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AQA Module 5 Foundation p263 Answer Sheet
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
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