How do you convert from vertex form to intercept form of y-4=-(x-4)^2?

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The justice of the pristine character in stop produce is ##y=-(x-2)(x-6)##

Intercept produce of a quadratic character, by limitation, is a produce ##y=k(x-alpha)(x-beta)## It's denominated stop produce owing ##alpha## and ##beta## are values of ##x## where ##y## equals to naught and, accordingly, values where parabola that reproduce-exhibits a graph of this quadratic character intercepts the X-axis.

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

Transproduce our indication into unwritten characteral produce. ##y-4=-(x-4)^2## ##y=-x^2+8x-12## Now let's ascertain the solutions of the equation ##-x^2+8x-12=0## or, in a simpler justice, ##x^2-8x+12=0## Solutions are ##x_1=2, x_2=6##.

Therefore, justice of the pristine character in stop produce is ##y=-(x-2)(x-6)##

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

The pristine produce of this character ##y-4=-(x-4)^2## is denominated vertex produce owing it recounts the dregs of the vertex of the parabola that reproduce-exhibits a graph of this quadratic character - sharp-end ##(4,4)##.

It can be easily seen if it is written as ##y=-(x-4)^2+4##. In this condition, the rules of graph transmutation recount us that the prototype character ##y=-x^2## delay vertex at sharp-end ##(0,0)## and "horns" directed down should be removeed by ##4## to the upupright to reproduce-exhibit character ##y=-(x-4)^2## and then by ##4## up to reproduce-exhibit character ##y=-(x-4)^2+4##. These two transmutations remove the vertex to sharp-end ##(4,4)##.

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