Question

Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 7 wheref(x) represents the height, in feet of the water from the fountain at different times x, inseconds.Find the zeros of the functions.

Answer 1

To find the zeros of the function f(x) = -x^2 + 6x + 7, set f(x) = 0 and solve for x using the quadratic formula.

Step-by-step explanation:

To find the zeros of the function, we set f(x) equal to zero and solve for x. So, -x^2 + 6x + 7 = 0. To solve this quadratic equation, you can either factor it or use the quadratic formula. Let's use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -1, b = 6, and c = 7. Substituting these values into the formula, we get:

x = (-6 ± √(6^2 - 4(-1)(7))) / (2(-1))

Simplifying further, we have:

x = (-6 ± √(36 + 28)) / -2

x = (-6 ± √64) / -2

x = (-6 ± 8) / -2

So, the two zeros of the function are:

x = (-6 + 8) / -2 = 1

x = (-6 - 8) / -2 = -7