MATHEMATICS
Quadratic Functions
Date: 2nd March 2010
Student name:
Class: MYP 4
The equation of a “quadratic function” is given by y = ax2 + bx + c, where a ≠ 0, and the graph of a
quadratic function is called a parabola.
If the coefficient of “x2” is positive, then the graph opens upwards, and if it is negative then the graph
opens downwards as shown below.
Quadratic graphs
positive quadratic y
= x2
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negative quadratic y = –x2
Date of issue: 11-Mar-19
-The point of intersection with the y-axis, where x = 0 is the y-intercept.
-The points of intersection with the x-axis, where y = 0 are called the x-intercepts, the ZEROS of the
function or roots of the equation.
- The vertex is the ‘turning point’ or the point at which the parabola changes its direction. [It can be
minimum or maximum]
- The x coordinate of the vertex is equal to:
and is also the midpoint of the roots (zeros) of the
equation, and the y-coordinate can be calculated by substituting with the x-coordinate in the equation.
-The vertical line that passes through the vertex is called the axis of symmetry
Quadratic Graphs
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Date of issue: 11-Mar-19
Draw the graphs of the following functions using a scale of 2cm for 1 unit on the x-axis and 1cm for 1
unit on y-axis.
For each graph state the following:
a) The y-intercept
b) The zeros of the equation
c) The equation of the axis of symmetry
d) The coordinates of the vertex and whether it is a maximum or minimum point
1. y = x2 + x – 2 , for -3 ≤ x ≤ 3
2. y = x2 +3x – 9 , for -4 ≤ x ≤ 3
3. y = x2 – 3x – 4 , for -2 ≤ x ≤ 4
4. y = 2 + x - x2 , for -3 ≤ x ≤ 3
5. y =3 + 3x - x2, for -2 ≤ x ≤ 5
6. y = 7 – 3x - 2x2, for -3≤ x ≤ 3
Quadratic Graphs
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Date of issue: 11-Mar-19