Question

The standard form of a quadratic function is f(x) = ax2 + bx + c. The characteristics listed below are

those of the graph of a specific quadratic function.
When x = 0, y 0
Explain your reasoning:
When y=0, x=(2, -3)
Which equation is correct for the given characteristics?
A. f(x) = -r-x+6
B. f(x) = x - x + 6
C. f(x) = -x*-1-6
D. f(x) = -x? +r+6

Answer 1

Non of the but it might be option A

Answer 2

None of the given options correctly represent the quadratic function with the characteristics of having the roots x = 2 and x = -3 and a y-intercept of (0,0). The equation based on these characteristics would be f(x) = a(x - 2)(x + 3), and since it passes through the origin, it simplifies to f(x) = ax(x + 1), which does not match any of the provided options.

Step-by-step explanation:

The student is asking how to find the correct equation for a quadratic function based on given characteristics. The standard form of a quadratic function is f(x) = ax² + bx + c. The graph of a quadratic function is a parabola, and it can open upwards or downwards. In this particular problem, we are given two key pieces of information: when x = 0, y = 0 and the roots of the equation (where y = 0) are x = 2 and x = -3.

To derive the correct equation, we can use the fact that if x = 2 and x = -3 are the roots of the quadratic function, then the function can be expressed as f(x) = a(x - 2)(x + 3). Since the y-intercept is (0,0), this means that the parabola passes through the origin and thus c = 0, simplifying our equation to f(x) = ax(x + 1).

No options provided match these criteria; however, the question contains typographical errors that may have misrepresented the options. Based on correct mathematical reasoning, none of the given options A, B, C, or D are valid equations for the characteristics provided