How do you write the function in standard form #y=-(9x+2)^2+4x#?

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Answer 1 · 2017-11-11T23:41:22

To put equations in standard form we must reorganize them from highest to lowest power.

#(9x+2)(9x+2) = 81x^2 + 36 + 4#

#y = - (81x^2+36x+4) + 4x #

distribute the negative to the parentheses

#y = -81x^2 color(red)(-36x) -4 + color(red)(4x)#

#y = -81x^2 -32x -4#

as you can see this a quadtratic function so our #y = 0# because a quadratic equation gives us the #x# values.

#0=-81x^2 -32x -4#

add everything to the #0# making terms positive (which is required for standard form)

#81x^2 + 32x +4 = 0#

as you can see it is now it is in order of highest powers to lowest and in standard form