Quadratic graphs

By Alex and Peter

Using Quadratic Equations to Get Information About a Graph

The Y Intercept

The Y intercept will always be the c in y = ax² + bx + c. For example, in the graph y = 2x² + 4x + 7, the y intercept will be 7 and in the graph y= -x² + x -12, the y intercept will be -12.

Minimum/Maximum Point

If the graph is is +ax², it will have a minimum point and if it is -ax², it will have a maximum point. To get the min/max point, you will need to find the completed square version of the quadratic equation. If the graph is y = a(x – h)² + k, the minimum point will be (h, k). For example, if the graph has the completed square form of y = -(x -1)² + 9, the maximum point will be (1, 9)

The Roots

To get the points that the line will pass through the x axis, you need to fully factorise the quadratic formula so that it looks something like y = (x + 1)(x – 2). In this graph the roots will be the two values for x which are -1 and 2 after you solve the equation y = 0.

Completing the Square

First we get the coefficient of the and look to see if it’s negative or can be factorised to become easier.  E.g. –x² – 2x – 5 this can be changed to -1(x² + 2x) – 5

Next we look at the coefficient of x and dividing everything by x that has an x and making the brackets squared.  E.g.-1(x² + 2x) – 5 which can be changed to -1((x + 1)² – 1) –  5

Then we multiply out the bracket and simplify. Be careful about multiplying the constant in the bracket by the -1.  E.g.  The example above becomes -1(x + 1)² – 4

Useful links:

http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/quadequationshirev2.shtml

http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=completingthesquare/square