Week 8 – Graphing Quadratic Equations

This week we started our new chapter analyzing quadratic equations. We learnt many trends and ways to look at the equation and just use that information to graph the function easily.

We start with are parent function y=

We know that the vertex is (0,0) because that is where the parabola switches directions.

This is the parent function and therefore follows the scale factor of 1 (1,3,5) Where you start at the vertex and go up move over one and place a dot and then go up 3 over 1 and place a dot. You would do this a few times and then connect the dots to form the parabola.

The domain is x is a set of all real numbers.

The range is y is greater or equal to zero. Because all the points on the parable are above zero.

The parabola opens up so the coefficient to x is positive.

The line of symmetry is x=0. The centre of the parabola falls on 0 on the x axis, dividing the parabola in half.

Now there a different equations that can change these things about the parabola.

y= +5  —> This equation changes the vertical translation of the parabola. It moves the parabola up or down the graph along the line of symmetry. Where the 5 will move the parabola up from points.

 

y=$latex y=(m-2)^2 —> This equation changes the horizontal translation of the parabola. It moves the parabola to the left or right on the graph. Where in this case the -2 will move the parabola 2 places to the right.

 

 

y= —> This equation changes the scale factor of the parabola. Stretching or compressing the parabola. In this case the scale factor is 2 which will change the pattern of the parabola. Instead of the pattern 1,3,5 it will be 2,6,10.