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Homework Statement
Find an equation of a parabola given three points without a vertex point.
Homework Equations
y=a(x-h)+k
The Attempt at a Solution
The parabola is upside down to I know a is negative.
The general form will give you your method. If you have three points, then you can form three equations in general form. The unknowns will be the coefficients. You can simply solve the system of linear equations. This would be introductory level algebra.I don't know how to find the variables given the three points.
You said you had 3 equations- you've only written 2 there!the 3 points are: (-2,2), (0,1), (1,-2.5)
I substituted the numbers, giving three equations.
2=4a-2b+c
1=0x^2+0b+C
-5/2=a+b+c
so c=1
-2b=-4a+1
b=(4a+1)/2
I can't get the numbers to work.
This is actually in my calculus book. chapter 1
Sorry, but it's too early to feel lucky! That's not at all right. Putting a= 2, b= 11/2, c= 1 into the first equation, you get 4(2)- 2(11/2)+ 1= 2- 11+ 1= -8, not 2.I got the numbers to work. The equation in general form is 2x^2-11/2x+1. How would I convert that to standard form. What is the trick to solving these? I feel like I got lucky to get the answer.
looks good to me.I think I switched the signs around. Now I get
2=4a-2b+c
1=0+0+c
-5/2=a+b+c
and got
a=-1
b=-5/2
c=1
Does that sound better?