Option A: The graph of the function intersect the x - axis at 2 points
Explanation:
Given that the function is [tex]y=2x^2-3x+1[/tex]
We need to determine the number of points that the graph of the function intersect the x - axis.
This can be determined by substituting [tex]y=0[/tex] in the function [tex]y=2x^2-3x+1[/tex]
Thus, we have,
[tex]0=2x^2-3x+1[/tex]
Factoring the expression, we have,
[tex]0=2x^2-2x-x+1[/tex]
Let us group the terms.
[tex]0=2x(x-1)+1(x-1)[/tex]
Factoring out the common term (x - 1), we have,
[tex]0=(x-1)(2x+1)[/tex]
Equating each term to zero, we have,
[tex]x-1=0[/tex] and [tex]2x+1=0[/tex]
[tex]x=1[/tex] and [tex]x=-\frac{1}{2}[/tex]
Thus, the graph of the function intersect the x - axis at 2 points.
Hence, Option A is the correct answer.
