what is the equation, in standard form, of a parabola that contains the following points. (-2,18),(0,2),(4,42)
A y=-2x^2-2x-3
B y=-3x^2+2x-2
C y=3x^2-2x+2
D y=-2x^2+3x+2

Question

what is the equation, in standard form, of a parabola that contains the following points. (-2,18),(0,2),(4,42)
A y=-2x^2-2x-3
B y=-3x^2+2x-2
C y=3x^2-2x+2
D y=-2x^2+3x+2

anonymous · Answer

i tried plugging x in but i keep getting wrong numbers

directrix · Answer

You may have to start with the general equation of a parabola:

y = ax^2 + bx + c

Substitute the three points:(-2,18),(0,2),(4,42) into the equation and solve for a, b and c.

whpalmer4 · Answer

Start out with the point $(0,2)$ which will give you the value of $c$ with no work.

$$y = ax^2+bx+c$$$$2 = a(0)^2+b(0)+c$$$$2=c$$

Now for the subsequent points you can use $$y = ax^2 + bx + 2$$

anonymous · Answer

can i just get a answer im tired of working on this equation

whpalmer4 · Answer

Yes, you can get an answer. Plug $(-2,18)$ into that formula, what do you get?

anonymous · Answer

i think its c but i keep getting random numbers

whpalmer4 · Answer

Well, let's say you've worked the problem and you think the answer is C, but you aren't sure.  How do you check it?  You plug in each of the points and see if they make true statements.
$$y = 3x^2-2x+2$$
point $(-2,18)$:

$$18 = 3(-2)^2 -2(-2)+2$$$$18 = 3(-2)(-2)-2(-2)+2$$$$18=12+4+2$$$$18=18\checkmark$$So far, the answer is okay, but it must work for all of the points.

point $(0,2)$:
$$2=3(0)^2-2(0)+2$$$$2=0-0+2$$$$2=2\checkmark$$
Also good.  

Now you just have one last point to check:
point $(4,42)$:

$$42=3(4)^2-2(4)+2$$

I'll let you decide if that works or not.

whpalmer4 · Answer

If you keep getting wrong or random numbers, you should show us an example so we can help you get the right numbers.  Telling you the answer to this problem won't really help you if you can't successfully do the problems.