Parabola help

Question

Given the equation -5 (x - 2)² -1=y
a. Identify the vertex.
b. Identify the axis of the symmetry.
c. Identify the direction of the graph (whether it opens up or down).

Answer 1

As I've mentioned in the previous problem, the general equation of a parabola that opens up or down is:

 

y=a(x-h)^2+k

 

If a is positive, it'll open up. If a is negative, it'll open down.

 

a.The vertex, (h,k) is in our case (2,-1)

 

b.The axis of symmetry, or the line that cuts right through the middle of your parabola is the vertical line x=2.

 

c.because -5<0, the parabola will open down.

 

(It opens down because the coefficient of x^2 is negative, so when x become really large -5x^2 will be really small, therefore our graph will have more negative y values and it will "go down".)