# What is the vertex form of #3y=-5x^2 - x +7#?

##### 1 Answer

Aug 5, 2017

#### Explanation:

Given:

#3y = -5x^2-x+7#

Divide both sides by

#y = 1/3(-5x^2-x+7)#

#color(white)(y) = -5/3(x^2+1/5x-7/5)#

#color(white)(y) = -5/3(x^2+2(1/10)x+1/100-141/100)#

#color(white)(y) = -5/3((x+1/10)^2-141/100)#

#color(white)(y) = -5/3(x+1/10)^2+141/60#

#color(white)(y) = -5/3(x-(-1/10))^2+141/60#

The equation:

#y = -5/3(x-(-1/10))^2+141/60#

is in the form:

#y = a(x-h)^2+k#

which is vertex form for a parabola with vertex

graph{3y = -5x^2-x+7 [-4.938, 5.06, -1.4, 3.6]}