Draw the graph of y = 2x^{2} 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.
x |
–3 |
–2 |
–1 |
0 |
1 |
2 |
3 |
y |
18 |
8 |
2 |
0 |
2 |
8 |
18 |
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 = ax^{2} (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.
Activity to Explore the Graph of a Quadratic Equation
The general form of a quadratic equation is y = ax^{2} + bx + c where a, b and c are real numbers and a is not equal to zero.
The following videos show how to Graph Quadratic Functions given in General Form.The general form of a quadratic equation isy = a(x + b)(x + c) where a, b and c are real numbers and a is not equal.
Graphing Parabolas in Factored Form y = a(x − r)(x − s)
The vertex form of a quadratic equation is
y = a(x − h)^{2} + k where a, h and k are real numbers and a is not equal to zero.
We can convert quadratic functions from general form to vertex form or factored form.
The following videos show how to Graph Quadratic Functions given in Vertex Form.
Graphing a Quadratic Function in Vertex Form
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