What is the vertex of y=3x22x(x+2)2?

2 Answers
May 11, 2017

The vertex is at (34,74)

Explanation:

y=3x22x(x+2)2

Expand the polynomial:
y=3x22x(x2+4x+4)

Combine like terms:
y=4x26x4

Factor out 4:
y=4[x2+32x+1]

Complete the square:
y=4[(x+34)2(34)2+1]

y=4[(x+34)2+716]

y=4(x+34)274

From vertex form, the vertex is at (34,74)

May 11, 2017

Vertex: (34,5516)(0.75,3.4375)

Explanation:

1) Rewrite this equation in standard form
y=3x22x(x+2)2
y=3x22x(x2+4x+4)
y=4x26x4

2) Rewrite this equation in vertex form by completing the square
y=(4x26x)4
y=4(x2+32x)4
y=4(x2+32x+(34)2)4+(34)2
y=4(x+34)25516

The vertex form is y=a(xh)2+k reveals the vertex at (h,k)

Vertex: (34,5516)(0.75,3.4375)

You can see this if you graph the equation
graph{y=-4x^2-6x-4 [-3, 2, -7, 0.1]}