What is the equation of the parabola that has a vertex at # (-4, 2) # and passes through point # (-8,-34) #?
1 Answer
Jun 21, 2018
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 multiplier"#
#"here "(h,k)=(-4,2)#
#y=a(x+4)^2+2#
#"to find a substitute "(-8,-34)" into the equation"#
#-34=16a+2#
#16a=-36rArra=(-36)/16=-9/4#
#y=-9/4(x+4)^2+2larrcolor(red)"in vertex form"#
#"expanding and rearranging gives"#
#y=-9/4(x^2+8x+16)+2#
#y=-9/4x^2-18x-34larrcolor(red)"in standard form"#
