Find a formula for the following function.
A parabola opening downward with its vertex at (6,1) and y -intercept equal to -35.
(y-1)^2=4(-35)(x-6) Please help
It means that y is equal to 3-1 times 2=4 times-35 times x-6.Use PEMDASLR to find your answer.
I agree that it is of form
(y-1)^2 = 4a (x-6)
but then when x = 0, y must be -35 so put that in
(-36)^2 = 4a (-6)
4a = - 216
so I think it is
(y-1)^2 = -4*54 (x-6)
Damon I respectfully disagree
Your parabola opens sideways
I think you meant to say:
y-1 = a(x-6)^2
then at (0,-35)
-36 = a(36)
a = -1
so y-1 = -(x-6)^2
y = -(x-6)^2 + 1
You are right, I was not thinking!
To find the formula for the given function, we can start by using the general equation for a parabola:
y = a(x-h)^2 + k
where (h, k) represents the vertex of the parabola. In this case, the vertex is given as (6, 1), so we have:
y = a(x-6)^2 + 1
Now, we need to determine the value of "a" to complete the equation. We can use the y-intercept to find this value.
The y-intercept is the point where the parabola intersects the y-axis, which occurs when x = 0. So, substituting x = 0 into the equation, we get:
-35 = a(0-6)^2 + 1
Simplifying this equation, we have:
-35 = 36a + 1
Subtracting 1 from both sides, we get:
-36 = 36a
Now, dividing both sides by 36:
-1 = a
Substituting this value of "a" back into the equation, we have:
y = -1(x-6)^2 + 1
Simplifying further, we get:
y = -(x-6)^2 + 1
This is the formula for the given parabola, with its vertex at (6, 1) and a y-intercept of -35.