Consider the quadratic function: f(x) = x2 – 8x – 9 vertex: what is the vertex of the function? ( , )

The vertex point of the function is (4 , -25)

Step-by-step explanation:

- Lets explain how to find the vertex of the quadratic function

- The form of the quadratic function is f(x) = ax² + bx + c , where

 a , b , c are constant

# a is the coefficient of x²

# b is the coefficient of x

# c is the y-intercept (numerical term)

- The x-coordinate of the vertex point is -b/a

- The y-coordinate of the vertex point is f(-b/a)

* Lets solve the problem

∵ f(x) = x² - 8x - 9

∴ a = 1 , b = -8 , c = -9

∵ The x-coordinate of the vertex point is -b/a

∴ The x-coordinate of the vertex point = -(-8)/2(1) = 8/2 = 4

- To find the y-coordinate of the vertex point substitute x by 4 in f(x)

∵ f(4) = (4)² - 8(4) - 9

∴ f(4) = 16 - 32 - 9

∴ f(4) = -25

∵ f(4) is the y-coordinate of the vertex point

∴ The y-coordinate of the vertex point is -25

∴ The vertex point of the function is (4 , -25)

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: