SOLUTION: 1) The length of a rectangular garden is 2 yd greater than the width. The area is 80 yd2. Find the length and width. I also have a next problem that an a little lost on: 2) G

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 1) The length of a rectangular garden is 2 yd greater than the width. The area is 80 yd2. Find the length and width. I also have a next problem that an a little lost on: 2) G      Log On

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Question 384116: 1) The length of a rectangular garden is 2 yd greater than the width. The area is 80 yd2. Find the length and width.
I also have a next problem that an a little lost on:
2) Given the quadratic equation y=2x^2+4x-1 find the coordinates of the vertex.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,
1) Let x and (x+ 2yd) represent the width and length respectively
x(x+2) = 80 yd^2
x^2 + 2x - 80 = 0
factoring
(x+10)(x-8) = 0 Note:SUM of the inner product(10*x) and the outer product(-8x) = 2x
(x+10)=0
x = -10 Tossing out negative solution
(x-8) = 0
x = 8yd , the width, the length 10yd (8yd + 2yd)
2)find the coordinates of the vertex:
the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex
y=2x^2+4x-1 Completing the square
y = 2[(x +1)^2 -1] - 1
y = 2(x+1)^2 - 2 - 1
y = 2(x+1)^2 - 3
Vertex Pt(-1,-3)
graph%28+300%2C+300%2C-6%2C6%2C-6%2C6%2C2x%5E2%2B4x-1%29+