Question

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

Answer 1

`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]}