Graphing Quadratics

Parabolas Any equation, where the highest power of x, is x2 when plotted on a graph, will form a parabola The simplest parabola is x -3 -2 -1 1 2 3 y=x2 9 4 1 1 4 9 We can see the shape looks like: Starting at the vertex Out 1 up 12 Out 2 up 22 Out 3 up 32 Out 4 up 42

x -3 -2 -1 1 2 3 y = -x2 -9 -4 -0 The graph is the same shape but upside-down The negative sign reflects the graph in the x axis

We can see the larger the number in front of the x2 The steeper the graph Remember the slope of linear graphs got steeper if we increased the number by the x These graphs are best plotted using points

x y=x2 y =2x2 Y=3x2 1 2 4 3 9 2 3 8 12 18 27

The graph is still reflected in the x axis We can see the larger the number in front of the x2 The steeper the graph Remember the gradient of linear graphs got steeper if we increased the number by the x

The smaller the number in front of the x2 the flatter the graph The ones with negative sign are reflected in the x axis

If we add a number to the x2 the parabola shifts up We can see: If we add a number to the x2 the parabola shifts up If we subtract a number from the x2 the parabola shifts down Note the shape is the basic Remember the correct word for shift is translate

We can also add numbers to the x before it is squared We can see the shape is the basic x2 shape If we add a number in the brackets the graph is translated to the left by the magnitude of the number If we subtract a number in the brackets the graph is translated to the right by the magnitude of the number

If we add a number in the brackets and at the end the graph is translated vertically and horizontally

We can also translate the reflected graphs

To draw Parabolas: Decide how it has been translated (find vertex) Decide if reflected in x axis (a<0) Stretched or compressed? Draw appropriate y = ax2 type from new vertex.

Parabolas in factorised form

E.g. 3

End Lesson Graphing Quadratics Homework: Page 47 #1-4, 9, 10.