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

##### 1 Answer

Jun 18, 2017

#### 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"#