What is the vertex form of y=6x2+11x+4?

1 Answer
Nov 29, 2017

the vertex form of the equation is
y=6(x+0.916666667)21.041666667

Explanation:

The general form of a quadratic equation is
y=ax2+bx+c

the vertex form of a quadratic equation is
y=a(xh)2+k

where (h,k) is the vertex of the line

for a standard quadratic the vertex of the line can be found where the slope of the line is equal to 0
The slope of a quadratic is given by the its first derivative
in this case
dydx=12x+11

the slope is 0 when x=1112or0.916666667

The original equation
y=6x2+11x+4

Substitute in what we know
y=6(1112)2+11(1112)+4=1.041666667

The vertex is at (0.916666667,1.041666667)

Thefore
the vertex form of the equation is
y=6(x+0.916666667)21.041666667