How do I find the equation for a parabola with one point and zeros?

Question

Link to the worksheet: http://primeruler.net/fall-break-project.pdf

Number 3 on page 4 asks to find an equation for a parabola that will get close enough to hit all three "pigs." For the zeros I was going to use (0,0) and (36,0) and then the one point it could pass through that would make it come close enough I estimated to be (25,6). How do I get a quadratic equation from those points?

OR, Is there a better way to do this?

Thanks.

scott8148 · Answer

2.(a) talks about the general equation for a parabola ___ y = ax^ + bx + c

plug the points into the general parabola equation to generate a system of linear equations
___ solve the system for  a, b, and  c

(22,6) ___ 6 = a(22)^2 + b(22) + c ___ 6 = 484a + 22b + c   (R)

(32,4) ___ 4 = a(32)^2 + b(32) + c ___ 4 = 1024a + 32b + c   (S)

(34,3) ___ 3 = a(34)^2 + b(34) + c ___ 3 = 1156a + 34b + c   (T)

subtracting R from S to eliminate c ___ -2 = 540a + 10b

subtracting S from T to eliminate c ___ -1 = 132a + 2b 
___ multiplying by 5 ___ -5 = 660a + 10b

subtracting equations to eliminate b ___ -3 = 120a

solve for  a , then substitute back to find  b  and  c

the "bird" marker is 2 units in diameter
___ this gives a fair amount of leeway for the guesstimation that the question suggests

Mercy · Answer

if the point given is the vertex:

https://www.google.ca/search?sourceid=navclient&aq=hts&oq=&ie=UTF-8&rlz=1T4GGNI_enCA530CA530&q=find+the+equation+for+a+parabola+with+one+point+and+zeros

Trending News

How do I find the equation for a parabola with one point and zeros?

2 Answers