SOLUTION: Use a system of linear equations to find the quadratic function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using matrices.
f(1) = 9, f(2) = 10,
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-> SOLUTION: Use a system of linear equations to find the quadratic function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using matrices.
f(1) = 9, f(2) = 10,
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Question 1178755: Use a system of linear equations to find the quadratic function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using matrices.
f(1) = 9, f(2) = 10, f(3) = 9 Found 2 solutions by MathLover1, ikleyn:Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!
that satisfies the given conditions. Solve the system using matrices.
, , ..........if , , ..........eq.1
..........if , , ...................eq.2
..........if , , .................eq.3
your system is:
..........eq.1 ...................eq.2 .................eq.3
--------------------------------------------------
Your matrix
Find the pivot in the 1st column in the 1st row
Eliminate the 1st column
Make the pivot in the 2nd column by dividing the 2nd row by
Let me show you how to solve it without using equations.
We have a parabola, and its ordinate y at x= 1 is the same as the ordinate y at x= 3.
It means that the parabola's symmetry axis is x= 2 half way between x= 1 and x= 3.
Hence, the parabola has a vertex at x= 10, and the vertex form equation is
y = a*(x-2)^2 + 10.
where "a" is a coefficient, now unknown.
To find "a", substitute x= 3 into the vertex form equation.
You will get then
9 = a*(3-2)^2 + 10, or
a*1^2 = 9 - 10
a = -1.
So, the vertex form equation is
y = -(x-2)^2 + 10.
Rewrite it in the general form
y = -(x^2 - 4x + 4) + 10 = -x^2 + 4x + 6.
Thus a= -1, b= 4, c= 6.
P L O T
Plot y = =
