Question

At how many points does the graph of the function below intersect the x-axis?

Answer 1

Option A: The graph of the function intersect the x - axis at 2 points

Explanation:

Given that the function is $y=2x^2-3x+1$

We need to determine the number of points that the graph of the function intersect the x - axis.

This can be determined by substituting $y=0$ in the function $y=2x^2-3x+1$

Thus, we have,

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

Factoring the expression, we have,

$0=2x^2-2x-x+1$

Let us group the terms.

$0=2x(x-1)+1(x-1)$

Factoring out the common term (x - 1), we have,

$0=(x-1)(2x+1)$

Equating each term to zero, we have,

$x-1=0$ and $2x+1=0$

     $x=1$ and        $x=-\frac{1}{2}$

Thus, the graph of the function intersect the x - axis at 2 points.

Hence, Option A is the correct answer.