What is the equation, in standard form, of a parabola that contains the following points?
(-2,-23.5), (0,-4.5), (4,-26.5)

a.) y=-2.5x^2+4.5x-4.5
b.) y=2.5x^2-4.5x+4.5
c.) y=-4.5x^2-2.5x-4.5
d.) y=4.5x^2+4.5x+2.5

WILL GIVE MEDALS

Question

What is the equation, in standard form, of a parabola that contains the following points? 
(-2,-23.5), (0,-4.5), (4,-26.5)

a.) y=-2.5x^2+4.5x-4.5
b.) y=2.5x^2-4.5x+4.5
c.) y=-4.5x^2-2.5x-4.5
d.) y=4.5x^2+4.5x+2.5

WILL GIVE MEDALS

anonymous · Answer

So the standard form is $$y=ax^2+bx+c$$

anonymous · Answer

You can make it a bit easier, though. Because "c" is where the function crosses the y-axis. So already know c, using this coordinate (0,-4.5)

anonymous · Answer

This way you can use the 2 other coordinates to make 2 equations with 2 variables. $$y=ax^2+bx-4.5$$. Try and insert the coordinates on x and y, and solve the system.

cmadaviss · Answer

How would I do that?

anonymous · Answer

So I insert the x and y values, and get the following equations: $$-23.5=a*(-2)^2+b*(-2)-4.5$$ $$-26.5=a*4^2+b*4-4.5$$ Now you need to solve for a and b, and you get your answer :)