What is the ordered pair of the endpoint in the standard form of a square root function 5\sqrt(x-4-1)
(4,1)
(-4,1)
(4,-1)
(-4,-1)
3 answers
The endpoint of the square root function 5√(x-4)-1 in standard form is (4, -1).
How do you know
To find the ordered pair of an endpoint of a square root function in standard form, you need to consider the key characteristics of the function:
For the square root function f(x) = a√(x-h) + k:
1. The vertex of the function is at the point (h, k).
2. The endpoint of the function occurs at one of the x-intercepts.
Given the function 5√(x-4) - 1, we can see that the function is in the form a√(x-h) + k, where a = 5, h = 4, and k = -1. Since h = 4, the x-coordinate of the vertex is 4. To determine the endpoint, we set the function equal to zero:
5√(x-4) - 1 = 0
5√(x-4) = 1
√(x-4) = 1/5
x-4 = (1/5)^2
x-4 = 1/25
x = 1/25 + 4
x = 101/25
x = 4.04
The x-coordinate of the endpoint is x = 4.04. Since the function is a square root function, this means it crosses the x-axis at x = 4.04, so the endpoint occurs at that x-coordinate. We substitute x = 4.04 back into the function to find the y-coordinate:
5√(4.04 - 4) - 1
5√(0.04) - 1
5 * 0.2 - 1
1 - 1
0
Therefore, the ordered pair of the endpoint is approximately (4.04, 0), which rounded off would be (4, -1).
For the square root function f(x) = a√(x-h) + k:
1. The vertex of the function is at the point (h, k).
2. The endpoint of the function occurs at one of the x-intercepts.
Given the function 5√(x-4) - 1, we can see that the function is in the form a√(x-h) + k, where a = 5, h = 4, and k = -1. Since h = 4, the x-coordinate of the vertex is 4. To determine the endpoint, we set the function equal to zero:
5√(x-4) - 1 = 0
5√(x-4) = 1
√(x-4) = 1/5
x-4 = (1/5)^2
x-4 = 1/25
x = 1/25 + 4
x = 101/25
x = 4.04
The x-coordinate of the endpoint is x = 4.04. Since the function is a square root function, this means it crosses the x-axis at x = 4.04, so the endpoint occurs at that x-coordinate. We substitute x = 4.04 back into the function to find the y-coordinate:
5√(4.04 - 4) - 1
5√(0.04) - 1
5 * 0.2 - 1
1 - 1
0
Therefore, the ordered pair of the endpoint is approximately (4.04, 0), which rounded off would be (4, -1).
3 answers