(-1/24)(x-12)^2 + 6
consists of two terms, so multiplying by 600 gives me
600 [ (-1/24)(x-12)^2 + 6] , now distribute ...
= -25(x-12)^2 + 3600
= -25(x^2 - 24x + 144) + 3600
= -25x^2 + 600x - 3600 + 3600
= -25x^2 + 600x
Find the point of intersection.
(-9/100)(x-10)^2+9=(-1/24)(x-12)^2+6
I don't understand how multiplying
y = (-1/2)(x-12)^2 + 6 by 600 would yield
-25(x-12)^2 + 3600 ? Is it supposed to yield
-300x^2+7200x-43,200+3600?
2 answers
( - 9 / 100 ) ( x - 10 ) ^ 2 + 9 = ( - 1 / 24 ) ( x - 12 ) ^ 2 + 6
- 9 * ( x ^ 2 - 2 * x * 10 + 10 ^ 2 ) / 100 + 9 = - 1 * ( x ^ 2 - 2 * x * 12 + 12 ^ 2 ) / 24 + 6
- 9 * ( x ^ 2 - 20 x * 10 + 100 ) / 100 + 9 = - 1 * ( x ^ 2 - 24 x + 144 ) / 24 + 6 Multiply both sides by 100 * 24
- 9 * 100 * 24 ( x ^ 2 - 20 x * 10 + 100 ) / 100 + 9 * 100 * 24 = - 1 * 100 * 24 ( x ^ 2 - 24 x + 144 ) / 24 + 6 * 100 * 24
- 9 * 24 ( x ^ 2 - 20 x * 10 + 100 ) + 9 * 2400 = -1 * 100 * ( x ^ 2 - 24 x + 144 ) + 6 * 2400
- 216 * ( x ^ 2 - 20 x * 10 + 100 ) + 21600 = -100 * ( x ^ 2 - 24 x + 144 ) + 14400
- 216 x ^ 2 + 4320 x - 21600 + 21600 = - 100 x ^ 2 + 2400 x - 14400 + 14400
- 216 x ^ 2 + 4320 x = - 100 x ^ 2 + 2400 x Add ( 100 x ^ 2 - 2400 x ) to both sides
- 216 x ^ 2 + 4320 x + 100 x ^ 2 - 2400 x = - 100 x ^ 2 + 2400 x + 100 x ^ 2 - 2400 x
- 116 x ^ 2 + 1920 x = 0 Divide both sides by 4
- 29 x ^ 2 + 480 x = 0
x ( - 29 x + 480 ) = 0
Solutions :
x = 0
and
- 29 x + 480 = 0 Subtract 480 to both sides
- 29 x + 480 - 480 = 0 - 480
- 29 x = - 480 Divide both sides by - 29
x = - 480 / - 29 = 480 / 29 = 16.551724
Now put x = 0 in equation
( - 9 / 100 ) ( x - 10 ) ^ 2 + 9
OR
( - 1 / 24 ) ( x - 12 ) ^ 2 + 6
all the same
y = 0
Put x = 489 / 29 in equation
( - 9 / 100 ) ( x - 10 ) ^ 2 + 9
OR
( - 1 / 24 ) ( x - 12 ) ^ 2 + 6
all the same
y = 4320 / 841 = 5.136742
Points of intersection:
x = 0 , y = 0
and
x = 489 / 29 , y = 4320 / 841
If you want to see graph go on :
wolframalpha dot com
When page be open in rectangle type :
(-9/100)(x-10)^2+9=(-1/24)(x-12)^2+6
and click option =
- 9 * ( x ^ 2 - 2 * x * 10 + 10 ^ 2 ) / 100 + 9 = - 1 * ( x ^ 2 - 2 * x * 12 + 12 ^ 2 ) / 24 + 6
- 9 * ( x ^ 2 - 20 x * 10 + 100 ) / 100 + 9 = - 1 * ( x ^ 2 - 24 x + 144 ) / 24 + 6 Multiply both sides by 100 * 24
- 9 * 100 * 24 ( x ^ 2 - 20 x * 10 + 100 ) / 100 + 9 * 100 * 24 = - 1 * 100 * 24 ( x ^ 2 - 24 x + 144 ) / 24 + 6 * 100 * 24
- 9 * 24 ( x ^ 2 - 20 x * 10 + 100 ) + 9 * 2400 = -1 * 100 * ( x ^ 2 - 24 x + 144 ) + 6 * 2400
- 216 * ( x ^ 2 - 20 x * 10 + 100 ) + 21600 = -100 * ( x ^ 2 - 24 x + 144 ) + 14400
- 216 x ^ 2 + 4320 x - 21600 + 21600 = - 100 x ^ 2 + 2400 x - 14400 + 14400
- 216 x ^ 2 + 4320 x = - 100 x ^ 2 + 2400 x Add ( 100 x ^ 2 - 2400 x ) to both sides
- 216 x ^ 2 + 4320 x + 100 x ^ 2 - 2400 x = - 100 x ^ 2 + 2400 x + 100 x ^ 2 - 2400 x
- 116 x ^ 2 + 1920 x = 0 Divide both sides by 4
- 29 x ^ 2 + 480 x = 0
x ( - 29 x + 480 ) = 0
Solutions :
x = 0
and
- 29 x + 480 = 0 Subtract 480 to both sides
- 29 x + 480 - 480 = 0 - 480
- 29 x = - 480 Divide both sides by - 29
x = - 480 / - 29 = 480 / 29 = 16.551724
Now put x = 0 in equation
( - 9 / 100 ) ( x - 10 ) ^ 2 + 9
OR
( - 1 / 24 ) ( x - 12 ) ^ 2 + 6
all the same
y = 0
Put x = 489 / 29 in equation
( - 9 / 100 ) ( x - 10 ) ^ 2 + 9
OR
( - 1 / 24 ) ( x - 12 ) ^ 2 + 6
all the same
y = 4320 / 841 = 5.136742
Points of intersection:
x = 0 , y = 0
and
x = 489 / 29 , y = 4320 / 841
If you want to see graph go on :
wolframalpha dot com
When page be open in rectangle type :
(-9/100)(x-10)^2+9=(-1/24)(x-12)^2+6
and click option =