I'm here to help with your math question. Let's break it down step by step.
1) Zeros of the function:
To find the zeros of the function g(r), you need to set g(r) equal to zero and solve for r.
Given: g(r) = r² - 6r - 55
Setting g(r) = 0:
r² - 6r - 55 = 0
Now, you can solve this quadratic equation to find the zeros.
2) To find the smaller r and larger r, you can factor the quadratic equation or use the quadratic formula:
r = [-b ± √(b² - 4ac)] / 2a
where a = 1, b = -6, and c = -55 in this case.
3) Vertex of the parabola:
The vertex of a parabola in the form y = ax² + bx + c can be found using the formula:
Vertex = (-b/2a, f(-b/2a))
For the given function g(r) = r² - 6r - 55, the vertex can be determined using this formula. The x-coordinate of the vertex is -(-6)/2(1), and the y-coordinate can be found by substituting this x-value back into the function g(r).
By following these steps, you will be able to find the zeros of the function and determine the vertex of the parabola accurately. If you need further assistance with the calculations or have any other questions, feel free to ask!
