Question

A quadratic function f(x) is hidden from view. You must find all intervals where f(x) is negative. Choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently.

Form: Standard Form
f(x)=2x²-16x - 30

Answer 1

To find the intervals where the quadratic function is negative, we can use the vertex form of the function and the quadratic formula.

Step-by-step explanation:

To find all intervals where the quadratic function f(x) = 2x² - 16x - 30 is negative, we need to determine the values of x for which f(x) is less than 0. One way to do this efficiently is by considering the vertex form of the quadratic function, which is f(x) = a(x - h)² + k.

In this form, the function is negative for values of x that are outside the interval (h - √(k/a), h + √(k/a)), where h is the x-coordinate of the vertex and k/a is the y-coordinate of the vertex.

In the given quadratic function, the coefficients are a = 2, b = -16, and c = -30. By using the quadratic formula to find the vertex, we can determine the values of h and k/a. Finally, we can identify the interval where f(x) is negative by considering the range of x values outside the interval (h - √(k/a), h + √(k/a)).