alex6799
  • alex6799
PLEASE HELP!!! Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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SolomonZelman
  • SolomonZelman
\(\large\color{#000000}{\displaystyle y= ax^2+bx+c }\) is what the quadratic equation looks like.
SolomonZelman
  • SolomonZelman
I got disconnected, apologize.
alex6799
  • alex6799
ok and then what? i have no idea on how to do this :(

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More answers

SolomonZelman
  • SolomonZelman
You are given 3 points so plug them in (individually) to solve for a, b, & c.
alex6799
  • alex6799
oh no worries its fine
SolomonZelman
  • SolomonZelman
plug in the points; For (-2,-20), \(\large\color{#000000}{\displaystyle -20= a(-2)^2+b(-2)+c }\) For (0,-4), \(\large\color{#000000}{\displaystyle -4= a(0)^2+b(0)+c }\) For (4,-20), \(\large\color{#000000}{\displaystyle -20= a(4)^2+b(4)+c }\)
SolomonZelman
  • SolomonZelman
Simplify and solve the system...
SolomonZelman
  • SolomonZelman
(note: it is very easy to obtain the c from the 2nd equation)
alex6799
  • alex6799
i dont understand
SolomonZelman
  • SolomonZelman
each of those points (-2, -20), (0, -4), (4, -20) is on the parabola, therefore, you can plug them into the parabola to solve for a, b and c. I plugged everything for you you just need to simplify and solve.
SolomonZelman
  • SolomonZelman
let's go with the first equation: \(\large\color{#000000}{\displaystyle -20= a(-2)^2+b(-2)+c }\) can you simplify this one?
alex6799
  • alex6799
ok i get that but how would i simplify them?
SolomonZelman
  • SolomonZelman
(-2)² = ?
alex6799
  • alex6799
4?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
\(\large\color{#000000}{\displaystyle -20= a(-2)^2+b(-2)+c }\) \(\large\color{#000000}{\displaystyle -20= 4a-2b+c }\)
SolomonZelman
  • SolomonZelman
\(\large\color{#000000}{\displaystyle -20= 4a-2b+c }\) is your first equation.. ok?
alex6799
  • alex6799
ok
SolomonZelman
  • SolomonZelman
Now simplify the second equation
alex6799
  • alex6799
\[-4=a+b+c\] ?
alex6799
  • alex6799
@SolomonZelman
SolomonZelman
  • SolomonZelman
\(\large\color{#000000}{\displaystyle -4= a(0)^2+b(0)+c }\) what is 0²?
alex6799
  • alex6799
0 right?
SolomonZelman
  • SolomonZelman
yes, and what is a times 0?
alex6799
  • alex6799
0
SolomonZelman
  • SolomonZelman
what is b•0 ?
alex6799
  • alex6799
0?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
So what does the second equatrion simplify to?
alex6799
  • alex6799
-4=a+c?
SolomonZelman
  • SolomonZelman
almost right
SolomonZelman
  • SolomonZelman
we said that 0²=0, and a•0=0, so what happens to the "a(0)²" component?
alex6799
  • alex6799
it goes away?
SolomonZelman
  • SolomonZelman
yes, so what is your second equation?
alex6799
  • alex6799
umm... -4=c?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
\(\large\color{#000000}{\displaystyle -20= 4a-2b+c }\) \(\large\color{#000000}{\displaystyle -4= c }\) now lets do the 3rd equation.
SolomonZelman
  • SolomonZelman
\(\large\color{#000000}{\displaystyle -20= a(4)^2+b(4)+c }\)
SolomonZelman
  • SolomonZelman
4² = ?
alex6799
  • alex6799
8?
alex6799
  • alex6799
wait no 16
SolomonZelman
  • SolomonZelman
yes 4² = 4•4 = 16
SolomonZelman
  • SolomonZelman
so your third equation, when simplified, would be?
alex6799
  • alex6799
\[-20=16a+4b+c\] ?
SolomonZelman
  • SolomonZelman
fabulous!
alex6799
  • alex6799
^-^
SolomonZelman
  • SolomonZelman
So we have, \(\large\color{#000000}{\displaystyle -20= 4a-2b+c }\) \(\large\color{#000000}{\displaystyle -4= c }\) \(\large\color{#000000}{\displaystyle -20=16a+4b+c }\)
SolomonZelman
  • SolomonZelman
Note (again), that in 2nd equation you are given the value of c explicitely: c=-4 And you can use that to solve the 1st and 2rd equations for "a" and "b".
SolomonZelman
  • SolomonZelman
plug in c=-4, into equation 1 and into equation 3.
alex6799
  • alex6799
so... \[-20=4a-2b+-4\] ?
SolomonZelman
  • SolomonZelman
yes, the first equation... and that would be better written as, \(\large\color{#000000}{\displaystyle -20=4a-2b-4 }\)
SolomonZelman
  • SolomonZelman
Now, plug in c=-4, into the 3rd equation, please..
alex6799
  • alex6799
\[-20=16a+4b+-4\] ?
SolomonZelman
  • SolomonZelman
YES! and that would be better written as?
alex6799
  • alex6799
@SolomonZelman ?

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