MATH SOLVE

5 months ago

Q:
# consider the quadratic function: f(x) = x2 – 8x – 9 Vertex: What is the vertex of the function? ( , )

Accepted Solution

A:

Answer: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)