1. ## Equation of parabola!

How the hell do you derive an equation from a graph?

For example this inverted parabola has x-intercepts at 0 and 2, but does that really mean that the equation is -x(x-2)?

Well it cant be, because the vertex is at (1,2), and -1(1-2)=1, not 2. How do you derive equations from graphs??

2. Originally Posted by olivia59
How do you derive an equation from a graph?

For example this inverted parabola has x-intercepts at 0 and 2, but does that really mean that the equation is -x(x-2)?

Well it cant be, because the vertex is at (1,2), and -1(1-2)=1, not 2. How do you derive equations from graphs??
x-intercepts at x = 0 and x = 2

y = kx(x-2) , where k is a constant TBD ....

vertex at (1,2) ...

2 = k(1)(1-2)

2 = -k

k = -2

equation is y = -2x(x-2)

3. Thanks, sorry.

4. Originally Posted by olivia59
How the hell do you derive an equation from a graph?

For example this inverted parabola has x-intercepts at 0 and 2, but does that really mean that the equation is -x(x-2)?

Well it cant be, because the vertex is at (1,2), and -1(1-2)=1, not 2. How do you derive equations from graphs??
Also "watch your language" in writing "the equation is -x(x-2)". That's not even an equation!

You meant "does that mean the equation is y= -x(x-2)?"

And the answer is "no". It means the equation is y= ax(x-2) where a is some negative number. You can use the fact that when x= 1, y= 2 to determine a: 2= a(1)(1- 2)= -a.