Question

Determine the number of x-intercepts of the graph of f(x)-ax²+bx+c (a40), based on the discriminant of the related equation f(x)=0. (Hint: Recall that the discriminant is b²-4ac.) /(x)=2x²+2x+1

Answer 1

The discriminant for the function f(x) = 2x² + 2x + 1 is negative, which indicates that the graph of this function has no real x-intercepts.

Step-by-step explanation:

The number of x-intercepts of a quadratic function can be determined by analyzing the discriminant of the quadratic equation, f(x) = ax² + bx + c. The discriminant is calculated using the formula b² - 4ac. If the discriminant is positive, there will be two x-intercepts; if it is zero, there will be exactly one x-intercept, and if it is negative, there will be no real x-intercepts.

In this case, the given function is f(x) = 2x² + 2x + 1. Applying the discriminant formula, we get b² - 4ac = (2)² - 4(2)(1) = 4 - 8 = -4. Since the discriminant is negative, the graph of the function does not cross the x-axis and therefore has no real x-intercepts.

Answer 2

The number of x-intercepts for a quadratic function can be determined using the discriminant. For the function f(x) = 2x² + 2x + 1, the discriminant is -4, indicating there are no x-intercepts.

Step-by-step explanation:

The number of x-intercepts of the graph of a quadratic function can be determined using the discriminant of the related equation, which is given by the formula b² - 4ac. For the quadratic function f(x) = ax² + bx + c, when f(x) = 0, the discriminant reveals the nature of its roots:

• If discriminant > 0, there are two distinct real roots, and hence two x-intercepts.
• If discriminant = 0, there is one real root, and hence one x-intercept (the graph touches the x-axis).
• If discriminant < 0, there are no real roots, and hence no x-intercepts (the graph does not intersect the x-axis).

In the case of the given function f(x) = 2x² + 2x + 1, we can calculate the discriminant using the coefficients a = 2, b = 2, and c = 1:

Discriminant = b² - 4ac = (2)² - 4(2)(1) = 4 - 8 = -4

Since the discriminant is less than 0, the graph of f(x) = 2x² + 2x + 1 has no x-intercepts.