What is the vertex form of y= 6x^2-9x+3 ?

2 Answers
Dec 14, 2017

y = 6(x-3/4)^2 - 3/8

Explanation:

To complete the square of the equation, first take out the 6:

y = 6(x^2 - 3/2x + 1/2)

Then do the bit in the brackets:

y = 6[(x-3/4)^2 - 9/16 + 1/2]

y = 6[(x-3/4)^2 - 1/16]

y = 6(x-3/4)^2 - 3/8 , as required.

Dec 14, 2017

y=6(x-3/4)^2-3/8

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"

"to obtain this form use the method of"
color(blue)"completing the square"

• " the coefficient of the "x^2" term must be 1"

rArry=6(x^2-3/2x)+3

• " add/subtract "(1/2"coefficient of x-term")^2" to"

x^2-3/2x

rArry=6(x^2+2(-3/4)xcolor(red)(+9/16)color(red)(-9/16))+3

rArry=6(x-3/4)^2-27/8+3

rArry=6(x-3/4)^2-3/8larrcolor(red)"in vertex form"