Embed Size (px)
DESCRIPTION
ALGEBRA MATHS
Citation preview
Quadratic EquationsQuadratic Equations
A term like x2 is called a square in algebra because it is the area of a square with side x
The adjective quadratic comes from the Latin word quadratum for square.
So a quadratic equation is one in which the highest indexnumber of a term with x in is x2
Examples of quadratic equations:y = x2
y = x2 + 1y = x2 + 3x - 10
Quadratic EquationsQuadratic Equations
These equations can be drawn as graphs in the same way that weknow how to draw straight line graphs.
x -3 -2 -1 0 1 2 3y
By substituting the given values for x calculate the y value for the following equation:
y = x2
9 4 1 0 1 4 9
This generates coordinates to plot on a graph
(-3,9)(-2,4)(-1, 1)(0, 0)
(1, 1)(2, 4)(3, 9)
Notice how the y valuesare symmetrical
Quadratic EquationsQuadratic EquationsPlotting these points
(-3,9)(-2,4)(-1, 1)(0, 0)
(1, 1)(2, 4)(3, 9)
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
x
x x
x xx
x
What is the name of this shape?Parabola
Why is it this shape?
because x2 is alwayspositive, even whenx itself is negativeand the value of y increases at a much faster rate than x
The lowest point is calledthe ‘minimum’
Quadratic EquationsQuadratic Equations
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Draw the graph for the following quadratic functiony = x2 + 1Complete the table:x -3 -1 0 1 3y 10 2 1 2 10
x
x xx
x
Draw the graph
Quadratic EquationsQuadratic Equations
Drawing graphs of more complex quadratic functionswe need bigger tables with more data in order to be ableto draw the graphs accurately
y = x2 - 3x - 2Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 4x2
-3x -2 y
16 9 4 1 0 1 4 9 1612 9 6 3 0 -3 -6 -9 -12 -2 -2 -2 -2 -2 -2 -2 -2 -2
Now add all thevalues togetherto find y 26 16 8 2 -2 -4 -4 -2 2
Quadratic EquationsQuadratic Equations
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Quadratic EquationsQuadratic Equations
y = x2 + 3Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 4x2 +3
y -4 -3 -2 -1 0 1 2 3 4
2018162
1412108642
-2 -4 -62
-8-10 -12-14-16-18-20
16 9 4 1 0 1 4 9 163 3 3 3 3 3 3 3 3
19 12 7 4 3 4 7 12 19
x
x
xx x x
x
x
x
Quadratic EquationsQuadratic Equations
y = x2 + 2x + 1Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 4x2
2x+1y -4 -3 -2 -1 0 1 2 3 4
10982
7654321
-1 -2 -32
-4 -5 -6 -7 -8 -9-10
16 9 4 1 0 1 4 9 16 -8 -6 -4 -2 0 2 4 6 8 +1+1 +1+1 +1 +1+1 +1+1 9 4 1 0 1 4 9 16 25
x
x
xx
x
x
x
Quadratic EquationsQuadratic Equations
y = 2x2 – x + 3Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 42x2 -x +3 y -4 -3 -2 -1 0 1 2 3 4
5045402
3530252015105
-5 -10 -152
-20 -25 -30 -35 -40 -45 -50
32 18 8 2 0 2 8 18 32+4+3 +2+1 0 -1 -2 -3 -4 +3+3 +3+3 +3+3+3+3+3 37 2413 6 3 4 9 18 31
X
X
XX X
X
X
XX
X
Quadratic EquationsQuadratic Equations
y = x2 + 3Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 4x2 +3
y -4 -3 -2 -1 0 1 2 3 4
2018162
1412108642
-2 -4 -62
-8-10 -12-14-16-18-20
Worksheet 1
Quadratic EquationsQuadratic Equations
Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 4x2 2x +1 y -4 -3 -2 -1 0 1 2 3 4
2018162
1412108642
-2 -4 -62
-8-10 -12-14-16-18-20
Worksheet 2
y = x2 + 2x + 1
Quadratic EquationsQuadratic Equations
Draw the graph of this function
x -4 -3 -2 -1 0 1 2 3 4
y -4 -3 -2 -1 0 1 2 3 4
10982
7654321
-1 -2 -32
-4 -5 -6 -7 -8 -9-10
y = 2x2 – x + 3
Worksheet 3
