SOLUTION: 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

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=
==
you need 3 sets of points, any 3 of the 5 sets given will do.
--
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
==
eq 1: 5=81a+9b+c
eq 2: 10=100a+10b+c
eq 3: 5=121a+11b+c
==
eq 4: 5=19a+b sub eq1 from eq2 to eliminate c
eq 5: 0=40a+2b sub eq1 from eq3 to eliminate c
==
-10=2a multiply eq4 by -2 and add to eq 5 to eliminate b
a=-5
==
substitute a=-5 into eq4 or eq5, i'll choose eq 5
0=40*(-5)+2b
0=-200+2b
200=2b
100=b
===
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
==
a=-5, b=100, c=-490
substitute into the standard equation
y=
==
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

RELATED QUESTIONS
The crop yield, Y, (in bushels) for various amounts, x (in pounds per 100 square feet) of (answered by stanbon)

Use the given data to find the equation of the regression line. Examine the scatterplot... (answered by CPhill)

The points in the table lies on a line. Find the slope-intercept form of the line. x 6 8 (answered by Alan3354)

Does the data in the table represent a direct or an inverse variation? Write an equation (answered by ewatrrr)

This table shows 10 observations of a pair of variables (x, y). The variables x and y are (answered by stanbon)

11-22 Sales of industrial vacuum cleaners at Overholt Supply Co. over the past 13... (answered by Alan3354)

The Problem: Farmer Fay has a pig that presently weighs 200 pounds. She could sell it now (answered by ikleyn)

Use the point-slope form linear equation given to complete problems 5-18 Y- 3 = 3(x +... (answered by solver91311)

Please help me out with this questions. I appreciate thanks. Based on the data shown... (answered by ewatrrr)