Does this function cross the x-axis twice?

Question

When graphed, does function below crosses the x-axis twice?

2x^2 - 3x + 1

*cross ...sorry =)

Answer 1

It crosses the x-axis when y = 0, so

0 = 2x^2 - 3x + 1.

The easiest way to solve this is to use the quadratic equation (unless you can see what the roots are):

(-b +/- sqrt (b^2 - 4ac)) / 2a from the form y = ax^2 + bx + c.
So, a = 2, b = -3, and c=1

(-(-3) +/- sqrt ( (-3)^2 - 4 (2) ( 1)) / 2(2)=
(3 +/- sqrt (9-8)) / 2 = (3 +/- 1) / 2
x = 1, 2.

So the function does cross the x-axis twice, at x = 1, and x =2.

Answer 2

it crosses if the equation has 2 different roots.

2x^2 - 3x + 1 =0

discriminant = 9 -8 =1
x1 = (3 -1)/4 =1/2
x2 = (3 +1)/4 =1

it crosses the x axis twice (at x =1/2 and x =1)

Answer 3

It has the shape of a U.

It starts above, crosses below once and then crosses back up.