Home > Algebra > Vertex Form of a Quadratic Equation

What is the vertex form of #3y=4x^2 + 9x - 1?

Answer 1

#y=color(green)(4/3)(x-color(red)((-9/8)))^2+color(blue)(""(-81/48))#
with vertex at #(color(red)(-9/8),color(blue)(-81/48))#

Remember our target form is #y=color(green)m(x-color(red)a)^2+color(blue)b#
with vertex at #(color(red)a,color(blue)b)#

#3y=4x^2+9x-1#

#rarr y=color(green)(4/3)x^2+3x-1/3#

#rarr y=color(green)(4/3)(x^2+9/4x)-1/3#

#rarr y=color(green)(4/3)(x^2+9/4xcolor(magenta)(+(9/8)^2))-1/3color(white)("xx")color(magenta)(-color(green)(4/3)*(9/8)^2)#

#rarr y=color(green)(4/3)(x+9/8)^2-1/3-27/16#

#rarr y=color(green)(4/3)(x-color(red)((-9/8)))^2-16/48-81/48#

#rarr y=color(green)(4/3)(x-color(red)((-9/8)))^2+color(blue)((-97/48))#

which is the vertex form with vertex at #(color(red)(-9/8),color(blue)(-97/48))#

I admit this is not very pretty, so here is a graph of the given equation to demonstrate that this answer is at least reasonable:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Kennedy Adams

The vertex form of the quadratic equation (3y = 4x^2 + 9x - 1) is (y = 4/3(x + 9/8)^2 - 265/96).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.