Therefore, the zeros of the function F(x) = x^2 + 2x - 15 are x = 3 and x = -5.
Since the parabola opens upwards, the vertex represents the minimum value of the function. Therefore, the function F(x) = x^2 + 2x - 15 has a minimum value of -16 at x = -1.
Explanation:
To find the zeros of the function F(x) = x^2 + 2x - 15, we need to solve for x when F(x) = 0.
So, setting the function equal to 0, we have:
x^2 + 2x - 15 = 0.
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, a = 1, b = 2, and c = -15. Plugging these values into the quadratic formula, we get:
x = (-2 ± √(2^2 - 4*1*(-15))) / (2*1),
x = (-2 ± √(4 + 60)) / 2,
x = (-2 ± √64) / 2,
x = (-2 ± 8) / 2.
So, the solutions for x are:
x = (-2 + 8) / 2 = 6 / 2 = 3,
x = (-2 - 8) / 2 = -10 / 2 = -5.
Therefore, the zeros of the function F(x) = x^2 + 2x - 15 are x = 3 and x = -5.
To find the maximum or minimum of the function, we can use the vertex form of a parabola which is given by: y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a determines the direction of the parabola.
In the given function F(x) = x^2 + 2x - 15, we can rewrite it in vertex form:
F(x) = (x^2 + 2x + 1) - 1 - 15,
F(x) = (x + 1)^2 - 16.
From this form, we can see that the parabola opens upwards, and its vertex is at (-1, -16).
Since the parabola opens upwards, the vertex represents the minimum value of the function. Therefore, the function F(x) = x^2 + 2x - 15 has a minimum value of -16 at x = -1.