parabolas
posted by Emma .
how do i find the equaion of the following parabolas?
1)intercepts at (2,0),(8,0) and (0,48)
2)turning point at (1,2) and passing through the origin.
can someone please teach me how to do this??thanks!
The first: Write you standard equation of a parabola (it has two x intercepts)
y= h(xb)^2 + k
You have three points.
Put those in the equations, you then have three equations, solve for h, b, k.
Example (first point)
0=h(2b)^2 +k
second point
0=h(8b)^2 + k
Third point
48=hb^2 + k
solve for h, b k There will be a lot of algebra here. A trick is to note it is symetrically about x=5, so b=5
then from the first equation k=9h then putting that in the third,
48= h259h or h= 4
solved.
You can also simplify matters by making use of the location of the zeroes. You know that they are at x = 2 and x = 8, so the function must be of the form:
y(x) = A (x2)(x8)
To find A you use that y(0) = 48 >
A = 3
Suppose you are given three points (x1,y1), (x2,y2) and (x3,y3) and y1, y2 and y3 are not zero. Then this trick doesn't work. However, you can still make this trick work as follows. Instead of the function y(x) you consider the function z(x) defined s:
z(x) = y(x)  y1.
Then z(x1) = 0, z(x2) = y2y1 and
z(x3)=y3y1
Because z(x) is zero at x = x1, you know that it contains a factor (xx1). If you divide z(x) by (xx1) you'll get a linear function. So, we define:
h(x) = z(x)/(xx1).
Then h(x2)= (y2y1 )/(x2x1)
and
h(x3)= (y3y1 )/(x3x1)
h(x) is linear, you know it's value at two points, so you can easily determine it.
good post.
Respond to this Question
Similar Questions

maths(urgent)thanks.
a parabola with turning point at (1,2) and passing through the origin.find the equation of this parabola. how do i do this? 
Algebra 2
I am creating a project for math in which I have to draw an object using: parabolas, hyperbolas, circles,etc. We use conic section equations to identify where they are on the graph. I have confusion about writing the equation of parabolas. … 
math
Question2; Consider the function f(x)= cos3x 4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. … 
math
hilp meeee trying .... Consider the two parabolas :y1=2x^23x1 and y2=x^2+7x+20. (a) Find the points of intersection of the parabolas and decide which one is greater than the other between the intersection points. (b) Compute the … 
math
hilp meeee trying .... Consider the two parabolas :y1=2x^23x1 and y2=x^2+7x+20. (a) Find the points of intersection of the parabolas and decide which one is greater than the other between the intersection points. (b) Compute the … 
math
weloo Consider the two parabolas :y1=2x^23x1 and y2=x^2+7x+20. (a) Find the points of intersection of the parabolas and decide which one is greater than the other between the intersection points. (b) Compute the area enclosed by … 
Math
Find the points of intersection of the parabolas y=1/2x^2 and y=11/2x^2. Show that at each of these points the tangent lines to the two parabolas are similar Answer (+1,1/2) Please show and explain all steps thank yo 
Algebra 2
Find the vertex of each of the following parabolas by averaging the x intercepts. Then write each equation in graphing form. Y=x^214x+40 
Algebra 2
Find the x and y intercepts for the following parabolas. y=(x+12)^2144 y=(x8)^24 
Algebra 2
Find the x and y intercepts for the following parabolas. y=(x+12)^2144 y=(x8)^4