What is the vertex form of #3y=8x^2 + 17x - 13?
1 Answer
Nov 25, 2015
The vertex form is
Explanation:
First, let's rewrite the equation so the numbers are all on one side:
#3y=8x^2+17x-13#
#y=(8x^2)/3+(17x)/3-13/3#
To find the vertex form of the equation, we must complete the square:
#y=(8x^2)/3+(17x)/3-13/3#
#y=8/3(x^2+17/8x)-13/3#
#y=8/3(x^2+17/8x+(17/8-:2)^2-(17/8-:2)^2)-13/3#
#y=8/3(x^2+17/8x+(17/8*1/2)^2-(17/8*1/2)^2)-13/3#
#y=8/3(x^2+17/8x+(17/16)^2-(17/16)^2)-13/3#
#y=8/3(x^2+17/8x+(289/256)-(289/256))-13/3#
#y=8/3(x^2+17/8x+(289/256))-13/3-(289/256*8/3)#
#y=8/3(x+17/16)^2-13/3-289/96#
#y=8/3(x+17/16)^2-235/32#