## swiftskier96 Group Title Help!?!?!?!? 16. What is the equation, in standard form, of a parabola that models the values in the table? x - [-2, 0, 4] f(x) - [4, -6, 70] y = 3x² + 4x – 6 y = 4x² + 3x – 6 y = 6x² + 3x – 4 y = –4x² – 3x + 6 one year ago one year ago

1. ZeHanz Group Title

Standard form is y=ax²+bx+c. You've got these points on it: (-2, 4), (0,-6) and (4,70). Just substitute these for x and f(x) in the standard formula. Hint: begin with (0,-6) for a quick start!

2. swiftskier96 Group Title

So id begin with something like -6 = 3(0)^2 + 4(0) - 6 and if i got -6, the equation would be right?

3. swiftskier96 Group Title

4. phi Group Title

yes, that is the easy way. notice that the last 2 equations will fail

5. phi Group Title

because with x=0, just ignore any term with x in it.

6. swiftskier96 Group Title

So you're saying it has to be either A or B?

7. phi Group Title

y = 3x² + 4x – 6 y = 4x² + 3x – 6 y = 6x² + 3x – 4 y = –4x² – 3x + 6 with x= 0 these turn into y= -6 y= -6 y= -4 y= +6 only the first two have y=-6.

8. phi Group Title

are you sure you don't have a typo in f(x) values?

9. swiftskier96 Group Title

Ok. How do i figure out which ones the right answer? No, those are the right values.

10. phi Group Title

test y = 3x² + 4x – 6 replace x with -2 y = 3* -2*-2 + 4*-2 + -6 what is that?

11. phi Group Title

Do I have to multiply and add little numbers for you ?

12. swiftskier96 Group Title

I got -38. I think thats wrong... Hold on. Ok seriously? Im trying to do it. Im not as stupid as you think i am. Just give me a second.

13. phi Group Title

I think you are smart, but don't like to do this stuff

14. phi Group Title

always do it in small methodical steps y = 3* -2*-2 + 4*-2 + -6 3 * (-2*-2) is 3*4 = 12 4*-2 is -8 -6 is -6 add up 12-8-6 = 12 -14 = -2

15. ZeHanz Group Title

y=ax²+bx+c. Point (0,-6), so x = 0, y = -6: $-6=a \cdot 0^2 + b \cdot 0 + c \Leftrightarrow -6 = c$ So now you know c = -6. Now try the next point, (-2, 4), so set x = -2 and y = 4 in y=ax²+bx-6:$4=a \cdot (-2)^2 + b \cdot -2 -6 \Leftrightarrow 4a-2b-6=4 \Leftrightarrow 4a-2b=10$Last point, (4, 70), so set x = 4 and y = 70:$70=a \cdot 4^2 + b \cdot 4 -6 \Leftrightarrow 16a+4b-6=70 \Leftrightarrow 16a+4b=76$So now you have to solve the system: 4a-2b=10 16a+4b=76

16. phi Group Title

which does not match 4 . so it looks like equation 2 is the answer we can check: y = 4x² + 3x – 6 replace x with -2: y = 4* -2*-2 +3 * -2 -6 type this into google 4* -2*-2 +3 * -2 -6=

17. swiftskier96 Group Title

I got 4.

18. phi Group Title

so it must be equation 2 if we really wanted to check we could replace x with 4, and we will get 70

19. ZeHanz Group Title

So now you have to solve the system: 4a-2b=10 multiply with 2 16a+4b=76 leave the same Then it is: 8a-4b=20 16a+4b=76 ----------- + 24a = 96, so a = 96/24 = 4 Plug a=4 in 4a-2b=10, this gives: 16-2b=10, so 2b=6 and b =3 Formula: y=ax²+bx+c, with a=4, b=3, c=-6: Answer: y = 4x²+3x-6, that's answer B.