graph the point 6,0; 12,0; 9,-9

Question

graph for function x2-18x+72 with the points of 6, 0; 12,0 and 9,-9

Answer 1

This is a quadratic equation, so it is a simple parabola with an axis of symmetry at -b/2a,
which is -(-18)/2(1) = 18/2 = 9, so the a is of symmetry is x= 9.

 

You already know that the value of the function at 9 is -9 because they gave you the point (9,-9) as a known value. That is the vertex, because it lies on the axis of symmetry x=9.

 

The leading coefficient a is 1 and 1>0, so the parabola opens upward. They have given you the two roots (6,0) and (12,0) which, gratifyingly, confirm the symmetry of your curve.

 

Three points are generally sufficient to sketch a parabola, but since (6,0) and (9,0) are so closely related, you may want to calculate another point.

Because the curve is symmetric, it will have the same value, y, for paired x values f(9+h) = f(9-h), which means if you calculate f(10) you will also know f(8). That also means that (6,0) and (9,0) are mirrored values.

 

Again, since the curve is symmetric, you may be better off calculating another point on either side of the parabola, in order to better capture the shape of the curve. Whatever value you choose, it will be mirrored across the axis of symmetry, so if you calculate a fourth value, you will automatically have a fifth.

Answer 2

Since I don't know what class you are taking or how much you know about parabolas, this is a simple explanation:

Plot those points in which (9,-9) is your vertex. The other two points indicate where the parabola crosses through the x-axis.