Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.
What is the equation of the function in vertex form?
The given values exist
x, f(x)
6, -2
7, 4
8, 6
9, 4
10, -2
The equation of the function in vertex form exists
f(x) = a(x - h)² + k
To estimate the values of a, h, and k,
When x = 6, f(x) = -2 then
-2 = a(6 - h)² + k
= (h²-12·h+36)·a + k.............(1)
When x = 7, f(x) = 4 then
4 = a( 7- h)² + k
= (h²-14·h+49)·a + k...........(2)
When x = 8, f(x) = 6
6 = a( 8- h)² + k ...........(3)
When x = 9, f(x) = 4.
4 = a( 9- h)² + k ..........(4)
When x = 10, f(x) = -2
-2 = a(10- h)² + k ...........(5)
Subtract equation (1) from (2)
4 - 2 = a( 7- h)² + k - (a(6 - h)² + k )
= 13·a - 2·a·h........(6)
Subtract equation (4) from (2)
a (9 - h)² + k - a( 7- h)² + k
32a -4ah = 0
Simplifying the equation, we get
4h = 32
h = 32/4 = 8
From equation (6) we have;
13·a - 2·a·8 = 6
-3a = 6
a = -2
From equation (1), we have;
-2 = -2 × ( 10- 8)² + k
-2 = -8 + k
k = 6
The value of k = 6.
The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.
To learn more about quadratic function refer to: https://brainly.com/question/25841119
#SPJ9
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
