Question

Find the solution(s) of the function f(x) = 5x^2 - 15.

Choose the description that explains how you could find the answer to this question.

A. Since this equation is a degree 2 polynomial, I know the shape of the graph would be a parabola. The "a" value is positive, so the parabola would be facing up. Knowing this, I would change the "x" variable to zero and solve for "y." The solutions are also known as roots or zeros. So, I would graph this equation and estimate where the parabola crosses the y-axis.

B. This question is asking for the maximum value of "x," so I would find the vertex. Since this equation is in standard form, -b would find the x-value of the vertex using 2a and then plug this value in to find the solutions.

C. This question is asking for a solution, and I know that solutions are the values of "x" which make the function equal to zero. The solutions of this equation can easily be found by using the square root method.

D. (None of the above)

Answer 1

To find the solution(s) for the function f(x) = 5x^2 - 15, the equation is set equal to zero, factored, and then solved to find the roots, resulting in x = ±√3.

Step-by-step explanation:

function f(x) = 5x^2 - 15 involves finding the values of x for which f(x) equals zero. These values are known as the roots or zeros of the function. One method to find the roots of a quadratic equation of the form ax2 + bx + c = 0 is to use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).

However, in this case, the quadratic equation can be simplified by factoring out the common factor of 5, resulting in 5(x2 - 3) = 0. From this, it's clear that the roots are where x2 = 3, or x = ±√3.