How do you write the quadratic #y=-x^2+4x+12# in vertex form?

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Answer 1 · 2018-05-19T17:49:06

#color(blue)[y=−(x−2)2+16]# is the vertex form

The vertex form of a quadratic function is given by

#color(blue)[y=a(x−h)2+k]#

where (h, k) is the vertex of the parabola.

when written in vertex form

(h, k) is the vertex of the parabola and x = h is the axis of symmetry

the h represents a horizontal shift (how far left, or right the graph has shifted from x = 0)

the k represents a vertical shift (how far up, or down the graph has shifted from y = 0)

Now let convert this #color(red)[y=−x2+4x+12]# into vertex form

#y=−x2+4x+12#

#y−12=−x2+4x#

#y−12=−(x2−4x)#

#y−12=−(x2−4x+4−4)#

#y−12=−(x2−4x+4)+4#

#y−16=−(x2−4x+4)#

#y−16=−(x−2)2#

#color(blue)[y=−(x−2)2+16]# is the vertex form

show the vertex in the figure below

graph{-x^2+4x+12 [-10.06, 15.25, 6.58, 19.25]}