SOLUTION: Hi, I'm having trouble with the problem h(x) = -16x^2 + 64x + 140 where h(x) equals the height. I'm trying to find the height, but I'm not sure how to. When asked to write the quad

Algebra ->  Vectors -> SOLUTION: Hi, I'm having trouble with the problem h(x) = -16x^2 + 64x + 140 where h(x) equals the height. I'm trying to find the height, but I'm not sure how to. When asked to write the quad      Log On


   

Question 1012194: Hi, I'm having trouble with the problem h(x) = -16x^2 + 64x + 140 where h(x) equals the height. I'm trying to find the height, but I'm not sure how to. When asked to write the quadratic function in vertex form I came up with f(x) = 16(x+2)^2-56.
Thanks.
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
You should study how to use Completing the Square to change from general form to standard (or vertex) form. Your book should discuss this; otherwise study here: This lesson INCLUDES how to complete the square and put function into standard form.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%29+=+-16x%5E2+%2B+64x+%2B+140 in vertex form
h%28x%29+=+%28-16x%5E2+%2B+64x%2Bb%5E2%29-b%5E2+%2B+140
h%28x%29+=+-16%28x%5E2+-4x-b%5E2%29-16%28-b%5E2%29+%2B+140
h%28x%29+=+-16%28x%5E2+-4x-2%5E2%29%2B16%2A2%5E2+%2B+140
h%28x%29+=+-16%28x+-2%29%5E2%2B64+%2B+140
h%28x%29+=+-16%28x+-2%29%5E2%2B204

vertex is at:
(2, 204)




Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, I'm having trouble with the problem h(x) = -16x^2 + 64x + 140 where h(x) equals the height. I'm trying to find the height, but I'm not sure how to. When asked to write the quadratic function in vertex form I came up with f(x) = 16(x+2)^2-56.
Thanks.
The height is represented by the y-coordinate of the VERTEX

The height, or y-coordinate of the VERTEX, or h(x) occurs at: x+=+-+b%2F2a -----> x+=+-+64%2F%282+%2A+-+16%29 ------> x+=+%28-+64%29%2F%28-+32%29 ------> x = 2

h%28x%29+=+-+16x%5E2+%2B+64x+%2B+140 

h%282%29+=+-+16%282%29%5E2+%2B+64%282%29+%2B+140 ------- Substituting 2 for x

h%282%29+=+-+16%284%29+%2B+64%282%29+%2B+140

h%282%29+=+-+64+%2B+128+%2B+140

h%282%29+=+204

The height, or y-coordinate of the VERTEX occurs at h(2), and is:highlight_green%28204%29

It is that simple!

If you NEED to write the quad function in VERTEX form, then that's another story, but you don't have to!