1. The document provides instructions for students to use a graphing calculator application called Nspire to explore and analyze graphs of quadratic equations. 2. Students are asked to vary the values of a, b, and c in different quadratic equations and record the shape of the graph, location of maximum/minimum points, and equation of the line of symmetry. 3. The summary explains that graphs of quadratic equations with a positive coefficient of x^2 open up and have a maximum point, while those with a negative coefficient of x^2 open down and have a minimum point. The graph is always symmetrical around the line of symmetry passing through the maximum or minimum point.

1. XINMIN SECONDARY SCHOOL
MATHEMATICS DEPARTMENT
Sec 2 Express
Worksheet: Graphs of Quadratic Equations
Name : ( ) Class: Date:
Steps to use Nspire
1. Start Nspire.
2. Open the file: Quadratic Equations.tns.
3. Explore the effects of a, b and c by moving the slider.
Self-Exploration
1. By varying the values of a, b, and c, complete the following table.
Quadratic Shape Coefficient Coordinates of Equation of the
Equations of x2 Max or Min point Line of Symmetry
(a) y = x2 + 1
(b) y = – x2 + 1
(c) y = x2 + 2x + 2
(d) y = 3 + 2x – 2x2
(e) y = x2 – 5x + 4
(f) y = 3x2 + 4x – 7
(g) y = x – 2x2
Graphs of Quadratic Functions pg 1

2. Summary of findings
1. When the coefficient of x2 is positive, the graph of the quadratic equation opens
and it has a point.
2. When the coefficient of x2 is negative, the graph of the quadratic equation opens
and it has a point.
3. The graph of a quadratic equation is symmetrical. The line of symmetry is parallel to the
axis and it passes through the point or the
point.
Exercise
1. Sketch the following graphs in the box provided indicate clearly the maximum or minimum points.
(a) y = x2 – 6x + 10 (b) y = – x2 – 6x – 11
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Graphs of Quadratic Functions pg 2