Question

F(x)=x^2+2x-15 determine zeros and the maximum or minimum

Answer 1

The zeros of the quadratic function are x = -4 and x = 3. The maximum or minimum point is (-1, -16).

Step-by-step explanation:

The zeros of a quadratic function can be found by setting the function equal to zero and solving for x. In this case, the quadratic function is f(x) = x^2 + 2x - 15. To find the zeros, we can set f(x) = 0:

x^2 + 2x - 15 = 0

Next, we can factor or use the quadratic formula to solve for x. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the quadratic equation x^2 + 2x - 15 = 0, a = 1, b = 2, and c = -15. Substituting these values into the quadratic formula, we get:

x = (-2 ± √(2^2 - 4(1)(-15))) / (2(1))

Simplifying further:

x = (-2 ± √(4 + 60)) / 2

x = (-2 ± √(64)) / 2

x = (-2 ± 8) / 2

Therefore, the zeros of the function f(x) = x^2 + 2x - 15 are x = -4 and x = 3.

To determine the maximum or minimum point of the quadratic function, we can use the vertex formula:

x = -b / (2a)

Plugging in the values a = 1 and b = 2 from our original quadratic function, we get:

x = -2 / (2(1))

x = -1

Therefore, the vertex of the quadratic function is at x = -1. To find the corresponding y-value, we can substitute x = -1 into the original equation:

f(-1) = (-1)^2 + 2(-1) - 15

f(-1) = 1 - 2 - 15

f(-1) = -16

So the maximum or minimum point of the function f(x) = x^2 + 2x - 15 is (-1, -16).