What is the vertex form of #2y=5x^2+8x − 4.#?

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Answer 1 · 2017-06-25T09:27:06

The vertex form is #y=5/2(x+4/5)^2-18/5#

Let simplify the equation by completing the squares

#2y=5x^2+8x-4#

Dividing by #2#

#y=5/2x^2+4x-2#

#=5/2(x^2+8/5x)-2#

Completing the squares, adding half of the coefficient of #x# to the square and removing it

#y=5/2(x^2+8/5x+4^2/5^2)-2-5/2*4^2/5^2#

#y=5/2(x^2+8/5x+16/25)-2-8/5#

Factorising

#y=5/2(x+4/5)^2-18/5#

This is the vertex form

graph{y=5/2(x+4/5)^2-18/5 [-8.89, 8.89, -4.444, 4.445]}