Respuesta :
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
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