Graphing Quadratic Functions

Quadratic Graphs Of The Form y = ax² ( a ≠ 0 )

Draw the graph of y = 2x² for ≤ x ≤ 3, using a scale of 1 cm to 1 unit on the x-axis and 1 cm to 5 units on the y-axis.

Solution:

Step 1 : Construct the table of values.

Step 2 : Plot the points on the graph.

Step 3 : Draw a smooth curve passing through the points.

The curves of the functions you have drawn so far are called parabolas.

From the example above, you may have noticed the following properties.
Refer to the following diagram when you study these properties.

1. The graphs of y = ax² (a ≠ 0) pass through the origin (0, 0).

2. The y-axis is the line of symmetry

3. (a) When a is positive, each graph has a lowest point (origin) and opens upwards. This point is known as the minimum point.

(b) The smaller the value of a, the wider the graph opens.

4. (a) When a is negative, each graph has a highest point (the origin) and opens downwards. This point is known as the maximum point.

(b) The smaller the value of , the wider the graph opens.

General Quadratic Graphs

The general form of a quadratic equation is y = ax² + bx + c where a, b and c are real numbers and a is not equal to zero.

Example:

Draw the graph of y = x² + 2, for –4 „ x „ 4. From the graph, find:
a) the value of y when x = 1.5.
b) the values of x when y = 12.
c) the smallest value of y and the corresponding value of x.

Solution:

Construct the table of values.

Plot the graph.

Scale:
x-axis: 1 cm to 1 unit
y-axis: 1 cm to 2 units

From the graph,
a) when x = 1.5, y is approximately equal to 4.3
b) when y = 12, x is approximately equal to 3.2 or –3.2
c) the smallest value of y is 2 and the corresponding value of x is 0

Videos

Using discriminants to graph parabolas -
Professor Edward Burger explains using discriminants to graph parabolas

Graphing some important functions - Ploting points. linear functions, quadratic functions, cubic functions, square root functions, absolute value functions
Professor Edward Burger explains graphing some important functions

Stretching a graph - Parabola shapes and cubic shapes
Professor Edward Burger explains stretching a graph.

Graphing quadratics using patterns - summary
Professor Edward Burger explains graphing quadratics using patterns.

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