Answer:
(y - 3)² = 12(x + 3)
Step-by-step explanation:
The focus is to the right of the vertex, so the parabola is sideways and opens to the right.
The conic form of a sideways parabola is
(y - k)² = 4p(x - h)
The vertex is at h = -3; k = 3
The focus is at (h + p, k) = (-3 + p, 3)
The vertex and focus are three units apart, so p = 3.
The equation of your parabola is
(y - 3)² = 12(x + 3)
The figure below shows the graph of your parabola with its focus and vertex.
Answer:
Proof in explanation.
Step-by-step explanation:
I'm going to attempt this by squeeze theorem.
We know that is a variable number between -1 and 1 (inclusive).
This means that .
for all value
. So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.
By squeeze theorem, if
and , then we can also conclude that
.
So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at .
.
We can finally conclude that by squeeze theorem.
Some people call this sandwich theorem.
