XINMIN SECONDARY SCHOOLMATHEMATICS DEPARTMENTSec 2 ExpressWorksheet: 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 Equations

Shape Coefficient of x2

Coordinates of Max or Min point

Equation of the 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

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