Download presentation

Presentation is loading. Please wait.

Published byShawn Rich Modified over 5 years ago

1
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 6.3 The quadratic function

2
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function The quadratic function takes the form f(x) = ax 2 + bx + c where a ≠ 0. The graph of a quadratic function has a characteristic shape. Whether the graph is or depends on the value of a as shown below. a > 0 a < 0

3
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function When the quadratic function is graphed, there are several key properties that need to be identified. These are as follows. axis of symmetry y-intercept x-intercepts vertex

4
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function At the y-intercept, the x-coordinate is 0. Therefore the value x = 0 can be substituted into the equation y = ax 2 + bx + c. This gives y = c. y-intercept

5
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function At the x-intercept, the y-coordinate is 0. Therefore the value y = 0 can be substituted into the equation y = ax 2 + bx + c. This gives ax 2 + bx + c = 0. x-intercepts

6
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function ax 2 + bx + c = 0 can sometimes be solved by factorizing to give a(x + p)(x + q) = 0. If it cannot be factorized, x can be found by using the quadratic formula

7
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function The axis of symmetry for the quadratic y = ax 2 + bx + c is found using the equation Because the graph is symmetrical, the axis of symmetry also passes through the point that is halfway between the two x-intercepts. axis of symmetry x-intercepts

8
Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 The quadratic function The vertex lies on the axis of symmetry, therefore its x-coordinate is also found by the formula To find the y-coordinate of the vertex, substitute the x-value found above into the equation of the quadratic y = ax 2 + bx + c. vertex axis of symmetry

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google