Write a two-column proof. Given: line BD bisects angle CBE. Prove: angle ABD approximately equal to angle FBD.

The proof is derived from the summarily following equations;

∠FBE + ∠EBD = ∠CBA + ∠CBD

∠FBE + ∠EBD = ∠FBD

∠CBA + ∠CBD = ∠ABD

Therefore;

∠ABD ≅ ∠FBD

Step-by-step explanation:

The two column proof is given as follows;

Statement                                       Reason          

bisects ∠CBE                            Given

Therefore;

∠EBD ≅ ∠CBD                                Definition of angle bisector

∠FBE ≅ ∠CBA                                Vertically opposite angles are congruent

Therefore, we have;

∠FBE + ∠EBD = ∠CBA + ∠CBD     Transitive property

∠FBE + ∠EBD = ∠FBD                    Angle addition postulate

∠CBA + ∠CBD = ∠ABD                   Angle addition postulate

Therefore;

∠ABD ≅ ∠FBD                                  Transitive property.

Remember that the vertex form of a parabola is where is the vertex of the parabola.

Now, to find the vertex of the parabola, we are going to use the vertex formula:

For a quadratic of the form , the vertex is given by:

in other words, we find by evaluating the function at

We know form our quadratic that and , so let's use our formula to find :

Now we can evaluate our function at to find :

Now, we can rewrite our parabola in vertex form:

, , and

We can conclude that the correct answer is: y = 6(x + 1)2 – 16