# How do you find the vertex of #(x + 6)^2 = -36(y − 3)#?

##### 1 Answer

vertex

#### Explanation:

**1. Expand both sides of the equation.**

#(x+6)^2=-36(y-3)#

#x^2+12x+36=-36y+108#

**2. Isolate for y.**

Recall that general equation for a quadratic equation in standard form is

#x^2+12x+36-108=-36y#

#x^2+12x-72=-36y#

#y=-1/36x^2-1/3x+2#

**3. Factor -1/36 from the first two terms.**

To find the vertex, we must complete the square. We can do this by first factoring

#y=-1/36(x^2+12x)+2#

**4. Rewrite the bracketed terms as a perfect square trinomial.**

The value of

#y=-1/36(x^2+12x+((12)/2)^2)+2#

#y=-1/36(x^2+12x+36)+2#

**5. Subtract 36 from the perfect square trinomial.**

We cannot just add

#y=-1/36(x^2+12x+36# #color(red)(-36))+2#

**6. Multiply -36 by -1/36 to move -36 out of the brackets.**

#y=-1/36(x^2+12+36)+2(-36)*(-1/36)#

**7. Simplify.**

#y=-1/36(x^2+12+36)+2[(-color(red)cancelcolor(black)36)*(-1/color(red)cancelcolor(black)36)]#

#y=-1/36(x^2+12+36)+2+1#

#y=-1/36(x^2+12+36)+3#

**8. Factor the perfect square trinomial.**

The final step to finding the vertex is to factor the perfect square trinomial. This will tell you the

#y=-1/36(x+6)^2+3#