## mskyeg 2 years ago What is the equation, in standard form, of a parabola that models the values in the table?

1. mskyeg

2. mskyeg

Possible answers: y = 6x^2 + 5x – 4 y = –4x^2 – 5x + 6 y = 5x^2 + 4x – 6 y = 4x^2 + 5x – 6

3. Godsgirl

Its the last one.

4. Godsgirl

All you have to do is substituted x for the numbers. When you do that to all the equations you will found out the last one works for all of them and tht is how you get f(x)

5. CliffSedge

@Godsgirl , what if there weren't multiple choice answers to test, how would you do it?

6. Godsgirl

Well they would give you the equation and tell you to figure out f(x) so what you would do is substituted the x with the numbers they give you and that is how you find f(x) and the you would add them to the chart.

7. CliffSedge

What I mean, @Godsgirl , is what if they did not give the equation. What if the only thing you had was the chart. Could you get the function from that?

8. Godsgirl

You have to have the equation to solve for the function. If you don't have that you would not be able to solve for the chart.

9. CliffSedge

That is false, @Godsgirl Your method is fine in this situation where you have choices of functions to test, but if all you had was the chart, then you can get the function from it. I can show you how if you are interested.

10. Godsgirl

sure

11. CliffSedge

The points are (-2,0), (0,-6), and (4,78). If these all fit into f(x)=ax^2+bx+c, then we have three equations: 0=a(-2)^2+b(-2)+c -6=a(0)^2+b(0)+c 78=a(4)^2+b(4)+c From the second equation, we see that the y-intercept is c=-6, this makes the other two equations become 4a-2b=6 16a+4b=84 This can be solved as a system of two linear equations to find a and b, and then you'll have your equation.

12. CliffSedge

Also note that you can fit other models to these points, such as y=ax^3+bx^2+cx+d or even x=ay^+by+c, etc.

13. Godsgirl

Oh okay I totally forgot about tht. Its been a while since I've been in high school. I see it now.

14. CliffSedge

Yep. That's why I don't like multiple-choice questions, it makes it to easy to guess-and-check, and doesn't teach the broader lesson.

15. Godsgirl

Haha I agree with you. I graduated early. I was 16 when I did and I got a full ride to my college.