Question

what is the equation in standard form of a parabola that contains the following points (-2,-20),(0,-4),(4,-20)

Answer 1

One of the several equations for a parabola is

y=a(x-h)^2+k. Note how there are three constants? They are a, h and k. a is the coefficient of the (x-h)^2 term. (h, k) is the vertex of the parabola.

Another equation is y-k=a(x-h)^2. Same thing, really.

Another would be the familiar y=ax^2 + bx + c.

Choose one of these to work with. You are given 3 points: (-2,-20), (0,-4) and (4,-20). Each such point gives you an x- and a y-value.

Write your equation 3 times, one for each point.

You will obtain 3 equations in 3 unknowns, which is enuf info to enable you to some for a, h and k.

Finally, write your equation for the parabola, substituting the values for a, h and k that you have calculated.

Answer 2

need help

Answer 3

have you wrote your 3 equations yet?

Answer 4

What @freckles said is your best way.

Answer 5

y=ax^2+bx+c

so if you plugged in (0,-4) what would you have ?

Answer 6

and then you do similar thing for the other points given to get your other two equations

Answer 7

You know that your quadratic\[y(x) = ax^2 + bx + c\] equation is in the form
and you know your 3 points are \[(x,y(x))\]

So just use those three points to write three equations.

Answer 8

y=0x^2+-4x+c I don't think I set this up correctly

Answer 9

how did you get a is 0 and b is -4?
if a is 0 you don't even have a quadratic


did you mean to replace y with -4 and x with 0 in since you have the ordered pair (0,-4)
?

Answer 10

" (-2,-20),(0,-4),(4,-20)"

Let's use the quadratic y=ax^2+bx+c to find a solution; we need to determine the values of a, b and c.

First point: (-2,-20). Obviously x=-2 and y=-20.
Substituting these values into y=ax^2+bx+c, -20 = a(-2)^2 + b(-2) + c.

Second point: (0,-4): y=-4 when x=0, so 0 + 0 + c = -4

Do the same thing for the third point. c is already known, so you should end up with two linear equations in a and b. Solve for a and b. You have plenty of methods from which to choose: addition/subtraction, graphing, substitution, matrices, etc.

List your a, b and c.

Write your equation: y=ax^2 + bx + c.

Answer 11

You have no grounds for assuming that a=0.

Answer 12

got it?

Answer 13

y = -2x^2 + 4x - 4

Answer 14

Was that meant to be your final answer the equation of the parabola?

If so, check your equation by substituting the coordinates of each of these points: (-2,-20),(0,-4),(4,-20). If your equation comes out being "true," then you know it's correct; otherwise it's not correct.

Once again, an example: Look at (4,-20). Do the coordinates of this point satisfy your equation, y = -2x^2 + 4x - 4? Let x=4. Does y come out to -20 (as it should)?