Who likes parabolas 3 multiple choice 1. what is the vertex of the parabola? y−3=12(x+5)^2 2. the equation of a parabola is y=12x2+6x+23 . what is the equation of the directrix? y = 5.5 y = 4.5 y = 2 y = 0.5 3.the equation of a parabola is 132(y−2)2=x−1 . what are the coordinates of the focus? (−7, 2) (1, 10) (1, −6) (9, 2)

Question 1) Vertex of the Parabola.



The vertex of the general parabolic equation:



lies at (h,k)

Comparing the given equation to general equation, we can write:

h = - 5
k = 3

So, the vertex of the given parabola will be (-5, 3)

Question 2) Equation of Directrix

The correct equation of the parabola is:



First we need to convert the equation to standard form as shown below:



The directrix of the general parabola of the form:



is y = k - p

Comparing equation of given parabola with general parabolic equation, we can write:
p =1/2
k = 5

So, equation of directirx will be:

y = 5 - 1/2 = 4.5

So, option B gives the correct answer.

Question 3) Focus of the parabola

The correct equation of the parabola is:



Comparing this equation to the general parabolic equation, we can write:
p=8
h =1
k = 2

The focus of the parabola will be at (h+p,k) = (9,2)

So the focus of the parabola is at (9,2)

Thus, option D gives the correct answer.