Question

How do you write `f(x) = -4x^2 - 16x + 3` in vertex form?

Answer 1

`f(x)=-4(x+2)^2+19`

Explanation:

`"for the standard form of a parabola " y=ax^2+bx+c`

`"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)`

`y=-4x^2-16x+3" is in standard form"`

`"with " a=-4,b=-16,c=3`

`rArrx_(color(red)"vertex")=-(-16)/(-8)=-2`

`"substitute into f(x) for y-coordinate"`

`rArry_(color(red)"vertex")=-4(-2)^2-16(-2)+3=19`

`rArrcolor(magenta)"vertex "= (-2,19)`

`"the equation of a parabola in "color(blue)"vertex form"` is.

`• y=a(x-h)^2+k`

where ( h , k ) are the coordinates of the vertex and a is a constant.

`"here " (h,k)=(-2,19)" and "a=-4`

`rArry=-4(x+2)^2+19larrcolor(red)" in vertex form"`