1. Quadratic 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 index
number of a term with x in is x2
Examples of quadratic equations:
y = x2
y = x2 + 1
y = x2 + 3x - 10

2. Quadratic Equations
These equations can be drawn as graphs in the same way that we
know how to draw straight line graphs.
By substituting the given values for x calculate the y value for
the following equation:
y = x2 x -3 -2 -1 1 2 3 y 9 4 1 1 4 9
This generates coordinates to plot on a graph
(-3,9)
(1, 1)
Notice how the y values
are symmetrical
(-2,4)
(2, 4)
(-1, 1)
(3, 9)
(0, 0)

3. The lowest point is called
Plotting these points
Quadratic Equations
(-3,9)
(1, 1)
(-2,4)
(2, 4) 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y
(-1, 1)
(3, 9) x x
(0, 0)
What is the name of
this shape? x x
Parabola x x
Why is it this shape? x
because x2 is always
positive, even when
x itself is negative
The lowest point is called
the ‘minimum’
and the value of y
increases at a much
faster rate than x

4. Draw the graph for the following quadratic function y = x2 + 1 x x
Quadratic Equations
Draw the graph for the following quadratic function 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y
y = x2 + 1 x x
Complete the table: x -3 -1 1 3 y 10 2 1 2 10 x x
Draw the graph x

5. Quadratic Equations
Drawing graphs of more complex quadratic functions
we need bigger tables with more data in order to be able
to draw the graphs accurately
Draw the graph of this function
y = x2 - 3x - 2 x -4 -3 -2 -1 1 2 3 4 x2
-3x y
Now add all the
values together
to find y 26 16 8 2 -2 -4 -4 -2 2

6. Quadratic Equations y x 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -21 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y

7. Draw the graph of this function y = x2 + 3 x -4 -3 -2 -1 1 2 3 4 x2 +3
Quadratic Equations x
Draw the graph of this function 20 18 16 14 2 12 10 8 6 4 -2 -4 -6 -8
-10
-12
-14
-16
-18
-20
y = x2 + 3 x -4 -3 -2 -1 1 2 3 4 x2 +3 y 16 9 4 1

8. Draw the graph of this function x
Quadratic Equations
Draw the graph of this function x 10 9 8 7 2 6 5 4 3 1 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
y = x2 + 2x + 1 x -4 -3 -2 -1 1 2 3 4 x2 2x +1 y

9. Draw the graph of this function y = 2x2 – x + 3 x -4 -3 -2 -1 1 2 3 4
Quadratic Equations
Draw the graph of this function 50 45 40 35 2 30 25 20 15 10 5 -5
-10
-15
-20
-25
-30
-35
-40
-45
-50 X
y = 2x2 – x + 3 x -4 -3 -2 -1 1 2 3 4
2x2 -x +3 y

10. Draw the graph of this function y = x2 + 3 x -4 -3 -2 -1 1 2 3 4 x2 +3
Quadratic Equations
Worksheet 1
Draw the graph of this function 20 18 16 14 2 12 10 8 6 4 -2 -4 -6 -8
-10
-12
-14
-16
-18
-20
y = x2 + 3 x -4 -3 -2 -1 1 2 3 4 x2 +3 y

11. Draw the graph of this function y = x2 + 2x + 1 x -4 -3 -2 -1 1 2 3 4
Quadratic Equations
Worksheet 2
Draw the graph of this function 20 18 16 14 2 12 10 8 6 4 -2 -4 -6 -8
-10
-12
-14
-16
-18
-20
y = x2 + 2x + 1 x -4 -3 -2 -1 1 2 3 4 x2 2x +1 y

12. Draw the graph of this function y = 2x2 – x + 3 x -4 -3 -2 -1 1 2 3 4
Quadratic Equations
Worksheet 3
Draw the graph of this function 10 9 8 7 2 6 5 4 3 1 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
y = 2x2 – x + 3 x -4 -3 -2 -1 1 2 3 4 y