Albert Teen YOU ARE LEARNING:     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 $x$ is $x^2$. They have a distinctive U-shaped curve, which is symmetrical.

Let's try the equation$y = x^2 + x$

1

This means that for every $x$ value....

... $y$ is the square of $x$ plus $x$ 2

What is $y$ equal to when $x=0$ ?  3

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

We can plot this point on the graph at the coordinates $(0,0)$ . 4

What is$y$ when $x=2$ ?  5

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

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

What is $y$ when $x=-1$ ?  7

So when $x=-1$ , $y=0$

We can plot this point on the graph at the coordinates $(-1,0)$ . Notice that the line crosses the x-axis twice! 8

Let's calculate one more point. What is $y$ when $x=-3$ ?  9

Nice!

Now we have enough points to join up to find the line $y=x^2+x$ 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 $y=x^2+x$ that we have already calculated. 2

Some values of $y$ are missing. What is $y$ when $x=-2$ ?  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 $x=3$ ? Give your answer in the form $(x, y)$.  5

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

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