Download presentation

1
**Graphs of quadratic functions**

2
**Plotting graphs of quadratic functions**

y = ax2 + bx + c (where a ≠ 0) A quadratic function in x can be written in the form: We can plot the graph of a quadratic function using a table of values. For example: Plot the graph of y = x2 – 4x + 2 for –1 < x < 5. x x2 – 4x + 2 y = x2 – 4x + 2 –1 1 2 3 4 5 1 1 4 9 16 25 Talk through the substitution for each value of x to give the corresponding value of y. Ask students if they can tell you between which values of x the roots will be. + 4 + 0 – 4 – 8 – 12 – 16 – 20 + 2 + 2 + 2 + 2 + 2 + 2 + 2 7 2 –1 –2 –1 2 7

3
**Plotting graphs of quadratic functions**

x –1 1 2 3 4 5 7 –2 y = x2 – 4x + 2 The points given in the table are plotted … y 6 … and the points are then joined together with a smooth curve. 5 4 3 The shape of this curve is called a parabola. Point out that, at this level, graphs are rarely plotted in this way but are usually sketched to show their shape relative to the x- and y-axes and their general features. When a sketch is required we only find the coordinates of the points where the function crosses the axes and the coordinates of any turning points. 2 1 It is characteristic of a quadratic function. –1 1 2 3 4 5 x –1

4
**Parabolas Parabolas have a vertical axis of symmetry …**

…and a turning point called the vertex. When the coefficient of x2 is positive the vertex is a minimum point and the graph is -shaped. When the coefficient of x2 is negative the vertex is a maximum point and the graph is -shaped.

5
**Graphs of the form y = ax2 + bx + c**

Change the values of a, b and c to observe how each one affects the shape and position of the parabola. In particular, draw students’ attention to the fact that when a is positive the parabola is -shaped and when a is negative the parabola is -shaped. Changing the value of a stretches or squeezes the graph. Note, too, that when a = 0 the function is no longer quadratic but linear.

Similar presentations

Presentation is loading. Please wait....

OK

6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas

6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Free ppt on brain machine interface software Ppt on air pollution act Ppt on unique identification system Ppt on power system stability using facts devices Ppt on save tigers in india download music Ppt on sales closing techniques Ppt on needle chest decompression Writing process elementary ppt on cells Ppt on grease lubrication manifold Ppt on turbo c compiler