Question 359435: Find a quadratic equation in standard form to model the data in the table.
x y
9 5
10 10
11 5
12 -10
13 -35
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! standard equation: y=
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you need 3 sets of points, any 3 of the 5 sets given will do.
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This will generate 3 equations in 3 unknowns
x=9, Y=5 plug this into the standard equation 5=81a+9b+c
x=10, y=10 plug into std equation 10=100a+10b+c
x=11, y=5 plug into std equation 5=121a+11b+c
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eq 1: 5=81a+9b+c
eq 2: 10=100a+10b+c
eq 3: 5=121a+11b+c
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eq 4: 5=19a+b sub eq1 from eq2 to eliminate c
eq 5: 0=40a+2b sub eq1 from eq3 to eliminate c
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-10=2a multiply eq4 by -2 and add to eq 5 to eliminate b
a=-5
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substitute a=-5 into eq4 or eq5, i'll choose eq 5
0=40*(-5)+2b
0=-200+2b
200=2b
100=b
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substitute a=-5, b=100 into one of the 3 original equations, i'll choose eq1
5=81(-5)+9(100)+c
5=-405+900+c
5=495+c
c=-490
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a=-5, b=100, c=-490
substitute into the standard equation
y=
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validate this equation by choosing a different point
x=12, y=-10
-5*(12)^2+100*12-490 does this equal y=-10????
i'll let you finish this validation
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