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Quadratic graphs
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YOU ARE LEARNING:

Quadratic Graphs

Quadratic Graphs

Quadratic Graphs

Quadratic graphs are curved graphs where the highest power of x is 2. We use a table of values to figure out each point on the graph.

Quadratics are any graph where the highest power of xx is x2x^2. They have a distinctive U-shaped curve, which is symmetrical.

Let's try the equationy=x2+xy = x^2 + x

1

This means that for every xx value....

... yy is the square of xx plus xx

2

What is yy equal to when x=0x=0 ?

3

So when x=0x=0 , y=0y=0

We can plot this point on the graph at the coordinates (0,0)(0,0) .

4

What isyy when x=2x=2 ?

5

So when x=2x=2 , y=6y=6

We can plot this point on the graph at the coordinates (2,6)(2,6)

6

What is yy when x=−1x=-1 ?

7

So when x=−1x=-1 , y=0y=0

We can plot this point on the graph at the coordinates (−1,0)(-1,0) . Notice that the line crosses the x-axis twice!

8

Let's calculate one more point. What is yy when x=−3x=-3 ?

9

Nice!

Now we have enough points to join up to find the line y=x2+xy=x^2+x

1

The easiest way to draw a quadratic is by first completing a table of values, then plotting the points and joining them up with a smooth curve.

In the table above we can see the values for y=x2+xy=x^2+x that we have already calculated.

2

Some values of yy are missing. What is yy when x=−2x=-2 ?

3

What will the y-coordinate be for when the x-coordinate is 1?

4

Finally, what will the point be along the curve at x=3x=3 ? Give your answer in the form (x,y)(x, y).

5

So here is the completed table of values for y=x2+xy=x^2+x.

You might notice that the values are symmetrical around x=−1,0x=-1, 0. This is because the line is a symmetrical curve!