# What is the equation of the parabola that has a vertex at # (2, -9) # and passes through point # (6, -4) #?

##### 1 Answer

Aug 18, 2017

#### Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

where (h , k ) are the coordinates of the vertex and a is a constant.

#"here "(h,k)=(2,-9)#

#rArry=a(x-2)^2-9#

#"to find a substitute "(6,-4)" into the equation"#

#-4=16a-9rArra=5/16#

#rArry=5/16(x-2)^2-9larrcolor(red)" in vertex form"#

graph{5/16(x-2)^2-9 [-20, 20, -10, 10]}