12y=(x-1)^2 -48 identify the vertex, focus, and directrix of the parabola

Vertex: (1,-4)

Focus: (1,-1)

Directrix: y = -7

Step-by-step explanation:

We have been given the equation of parabola

Divide both sides by 12 to get the equation in vertex form

The vertex form of the parabola is

, where (h.k) is the vertex.

On comparing, we get

Vertex = (h,k) = (1,-4)

Now, we know that focus always lie inside the parabola and directrix is always outside the parabola.

Also, the vertex is the mid point of focus and the point on directrix. All three lie on the same line called axis of symmetry. The distance between focus and vertex is p

Thus, the focus is at 3 units upward from vertex

Focus is given by

And the directrix is a parallel line to x axis and at a distance of 3 units down from the vertex.

Hence, directrix is

y = -4-3

y = -7

560

hope this : )

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc