The graph of f crosses the x-axis at points where f(x)=0.
In this case f(x)=2x^2-3x+2 is quadratic, so we can look at the discriminant to find the number of x-intercepts.
2
&Quadratic equation: && ax^2+ bx+ c=0
&Solutions:&&x=- b±sqrt(b^2-4 a c)/2 a
&Discriminant:&& b^2-4 a c
The table below summarizes the relationship between the discriminant and the number of real solutions.
Discriminant (b^2-4ac)
Number of Real Solutions
Positive
2
Zero
1
Negative
0
Let's identify the coefficients in our expression.
2x^2-3x+2= 2x^2+( -3)x+ 2
We can see that a= 2, b= -3, and c= 2. Let's find the discriminant.
