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

May 19, 2018

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

#### Explanation:

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]}