# What is the equation of the parabola that has a vertex at # (-6, 3) # and passes through point # (12,9) #?

##### 1 Answer

Aug 3, 2018

#### Explanation:

#"the equation of a parabola in "color(blue)("vertex form"# is.

#•color(white)(x)y=a(x-h)^2+k#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is a multiplier"#

#"here "(h,k)=(-6,3)#

#y=a(x+6)^2+3#

#"to find a substitute "(12,9)" into the equation"#

#9=18a+3#

#18a=9-3=6rArra=6/18=1/3#

#y=1/3(x+6)^2+3larrcolor(red)"in vertex form"#

#"distributing gives"#

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

#y=1/3x^2+4x+15larrcolor(red)"in standard form"#