Final answer:
The quadratic function intersects the x-axis 2 times.
Step-by-step explanation:
The quadratic function y = 2x^2 + 7x + 6 can intersect the x-axis either zero, one, or two times. To determine the number of intersections, we can count the number of distinct x-intercepts of the function. An x-intercept occurs when the value of y is equal to zero. So, we can set the quadratic function equal to zero and solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the coefficients from the given function (a = 2, b = 7, and c = 6), we can substitute them into the quadratic formula and calculate the discriminant (b^2 - 4ac) to determine the number of x-intercepts.
If the discriminant is positive, there are two distinct x-intercepts. If the discriminant is zero, there is one x-intercept (the graph touches the x-axis at a single point). If the discriminant is negative, there are no x-intercepts (the graph does not intersect the x-axis).
In this case, the discriminant is positive, so the quadratic function intersects the x-axis 2 times. Hence, the answer is C. 2.