Question

A teacher writes the function f(x)=3x^2-18x+27 on the board. How many times does the graph of the teacher's function intersect the x-axis

Answer 1

Once. at (3,0)

Explanation:

It is handy to have a graphing calculator for this kind of question.

Otherwise work it out.

All the terms are multiples of 3, so simplify.
`3(x^(2) -6x + 9)`

then factor (x -3)(x-3)

Set each equal to 0 and solve for x.

x - 3 = 0 x = 3

OH ! they are identical! So there is only One value for x that will produce an output of 0.

So it intersects (touches) only once.