How do i find the equation in the form:
y=a(sqrt b(x-h))+k
From the points (-5,3) (-4,-1) (-1,-5)
To find the equation in the form y = a(sqrt(b(x-h))) + k, we need to determine the values of a, b, h, and k.
Step 1: Find the value of "a":
To find the value of "a," we can use one of the provided points. Let's choose the point (-5, 3). Substitute the x and y coordinates into the equation y = a(sqrt(b(x-h))) + k:
3 = a(sqrt(b(-5 - h))) + k
Step 2: Find the value of "b":
Similarly, we can use another point to find the value of "b." Let's use the point (-4, -1):
-1 = a(sqrt(b(-4 - h))) + k
Step 3: Find the value of "h":
To find the value of "h," we need to set up two equations using the remaining points (-4, -1) and (-1, -5). We can use the substitution method to solve for "h".
For point (-4, -1):
-1 = a(sqrt(b(-4 - h))) + k
For point (-1, -5):
-5 = a(sqrt(b(-1 - h))) + k
Solve this system of equations to find the value of "h" using elimination or substitution.
Step 4: Find the value of "k":
Having found the value of "h," we can substitute it back into one of the equations from Step 3 and solve for "k."
Once you have determined the values of a, b, h, and k, you can substitute them into the equation y = a(sqrt(b(x-h)))+k to obtain the equation in the required form.