Which of the following equations is of a parabola with a vertex at (0, 6)? y = (x - 6)2 y = (x + 6)2 y = x2 - 6 y = x2 + 6

The equation of a parabola with a vertex at (0, 6) is:

We know that the general equation of a upward or a downward parabola is given by:

where if a>0 then it is a upward open parabola.

and if a<0 then it is a downward open parabola.

Also, we have vertex at (h,k)

Now we are given that the vertex is at (0,6)

and also by looking at the options we see that a=1

Hence we have:

h=0 and k=6

Hence, the equation of the parabola is:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: