SOLUTION: A parabola whose axis is parallel to the y-axis passes through the points (1,1), (2,2) and (-1,5). Find its equation.
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Question 948208: A parabola whose axis is parallel to the y-axis passes through the points (1,1), (2,2) and (-1,5). Find its equation.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A parabola whose axis is parallel to the y-axis passes through the points (1,1), (2,2) and (-1,5). Find its equation.
--------------------
Form::
ax^2 + bx + c = y
-----
Using (1,1) u get:: a + b + c = 1
Using (2,2) u get: 4a + 2b + c = 2
Using (-1,5) u get: a - b + c = 5
----------------
Using a Matrix Program I get::
a = 1
b = -2
c = 2
------------
Equation:
y = x^2 - 2x + 2
=====================
Cheers,
Stan H.
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Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
use given points to set up the system of equations to find ,,and
(, ) ---->
(,) ---->
(,) --->
Solve simultaneous equations:subtract first from second one
...solve for
=>
=>.......1a
add first and third one:
....solve for
=>
=>.........2a
go to first eq., substitute from 1a
....solve for
...............1b
go to eq.2, substitute from 2a and from 1b
now find
=>
=>
=>
and
=>
=>
so, your equation is:
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