Question

question 7 of 10
at how many points does the graph of the function below intersect the x-axis?
y = 2x² - 3x + 1
a. 2
b. 0
c. 1

Explanation:

Step1: Recall the discriminant formula

For a quadratic function \(y = ax^2 + bx + c\), the discriminant is \(D = b^2 - 4ac\).

Step2: Identify coefficients

In \(y = 2x^2 - 3x + 1\), \(a = 2\), \(b = -3\), \(c = 1\).

Step3: Calculate the discriminant

\(D = (-3)^2 - 4\times2\times1 = 9 - 8 = 1\).

Step4: Analyze the discriminant

Since \(D = 1>0\), the quadratic equation \(2x^2 - 3x + 1 = 0\) has two distinct real roots, meaning the graph intersects the x - axis at 2 points.

Answer:

A. 2