1. Lesson 4

1.4. Discover

Mathematics 20-2 M3 Lesson 4

Module 3: Quadratics

 
Discover
 

In Lesson 1 you investigated how changing the coefficients and constant in the standard form of a quadratic function affects the shape of the graph. From these observations, you were able to identify characteristics of the graphs of quadratic functions written in standard form, y = ax2 + bx + c.

 

You discovered the following characteristics of a graph of a quadratic function that is defined by the equation y = ax2 + bx + c.

  • When a is greater than zero, the parabola opens up and the vertex is a minimum.

  • When a is less than zero, the parabola opens down and the vertex is a maximum.

  • The constant term, c, is the value of the parabola’s y-intercept.

  • The parabola is symmetrical about the vertical axis of symmetry.

  • The vertex is a point on the axis of symmetry.
This shows a graph. The parabola is opening upward. Its vertex is labelled minimum value, and a y-intercept is labelled c value. It is under the heading a > 0.

Adapted from: CANAVAN-MCGRATH ET AL. Principles of Mathematics 11,
© 2012 Nelson Education Limited. p. 323. Reproduced by permission.

 

This shows a graph. It has a downward opening parabola, Its vertex is labelled maximum value, and its y-intercept is labelled c value. It is under the heading a < 0.

Adapted from: CANAVAN-MCGRATH ET AL. Principles of Mathematics 11,
© 2012 Nelson Education Limited. p. 323. Reproduced by permission.