Question

Use the parabola tool to graph the quadratic function f(x)=(x−2)(x−6) . Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answer 1

Where's the so-called "parabola tool?"

The vertex is relatively easy to find. Find the midpoint of the segment of the x-axis connecting x=2 and x=6; it is x=4. Then evaluate the function at x=4:

f(4) = (4-2)(4-6) = 2(-2) = -4. The vertex is at (4,-4).

Plot (4,-4). Then (arbitrarily) let x=0 and find y: f(0) = y = (-2)(-6) = -12.
So, when x = 0, y = -12.

Plot this point (1, -12). realize that the parabola is symmetric about the line x=4. (1,-12) is 3 units to the left of the axis of symm, and thus another point on the parab. is 3 units to the right of this axis, x= 7. Plot (7,-12). Now draw the parabola thru (7,-12), (1, -12) and (4, -4). The parab. opens up.