# How do you convert from vertex arrange to catch arrange of ##y-4=-(x-4)^2##?

The truthfulness of the first part in catch arrange is ##y=-(x-2)(x-6)##

Catch arrange of a quadratic part, by specification, is a arrange ##y=k(x-alpha)(x-beta)## It’s denominated catch arrange consequently ##alpha## and ##beta## are values of ##x## where ##y## equals to naught and, hence, values where parabola that resembles a graph of this quadratic part intercepts the X-axis.

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In other suffrage, ##alpha## and ##beta## are solutions to an equation ##k(x-alpha)(x-beta)=0##

Transarrange our countenance into unwritten partal arrange. ##y-4=-(x-4)^2## ##y=-x^2+8x-12## Now let’s meet the solutions of the equation ##-x^2+8x-12=0## or, in a simpler truthfulness, ##x^2-8x+12=0## Solutions are ##x_1=2, x_2=6##.

Therefore, representation of the first function in catch arrange is ##y=-(x-2)(x-6)##

The graph of this part follows (attend-to the sharp-ends where it catchs the X-axis are ##x=2## and ##x=6##). graph{ -(x-4)^2+4 [-10, 10, -5, 5]}

The first arrange of this part ##y-4=-(x-4)^2## is denominated vertex arrange consequently it narrates the subsidence of the vertex of the parabola that resembles a graph of this quadratic part – sharp-end ##(4,4)##.

It can be easily seen if it is written as ##y=-(x-4)^2+4##. In this contingency, the rules of graph intercharge narrate us that the prototype part ##y=-x^2## with vertex at sharp-end ##(0,0)## and “horns” directed down should be removeed by ##4## to the straight to resemble part ##y=-(x-4)^2## and then by ##4## up to resemble part ##y=-(x-4)^2+4##. These two intercharges remove the vertex to sharp-end ##(4,4)##.

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