Question

The quadratic function f(x) has roots of ?4 and 3 and point (2, ?6) lies on f(x). what is the equation of f(x)?

1) f(x) = (x 3)(x ? 4)
2) f(x) = (x ? 3)(x 4)
3) f(x) = 3(x 3)(x ? 4)
4) f(x) = 3(x ? 3)(x 4)

Answer 1

The quadratic function f(x) with roots -4 and 3 and passing through the point (2, -6) has an equation f(x) = -(x + 4)(x - 3), which is not one of the provided options.

Step-by-step explanation:

The quadratic function f(x) has roots of -4 and 3, which means the factored form of the quadratic equation can start with f(x) = (x + 4)(x - 3). However, we need to find the correct equation that includes the point (2, -6). To determine the right equation, we substitute x=2 into the equation and set f(x) to -6, which gives us -6 = (2 + 4)(2 - 3). Simplifying this we get -6 = (6)(-1), which is 6, not -6. Therefore, there must be a coefficient in front of the factored form to adjust for this discrepancy.

Let A be the coefficient we're looking for. We then have f(x) = A(x + 4)(x - 3). Substituting the point (2, -6) into the equation gives us -6 = A(2 + 4)(2 - 3). We find that A = -6/6 = -1. Therefore, the correct equation for f(x) is f(x) = -(x + 4)(x - 3) or f(x) = (-1)(x + 4)(x - 3), which is not one of the provided options.