Question

Please Help!! And show work so I can figure how to do the next on my own.



What is the equation, in standard form, of a parabola that models the values in the table?

Answer 1

What table??

Answer 2

The table looks like this
x -2 0 4
F(x)1 5 -59

Answer 3

the general form of a parabola is
f(x) = ax^2+bx+c

now we have to satisfy the conditions :

f(-2) = 1
f(0) = 5
f(4) = -59

using this we will find a,b,c

Answer 4

x f(x)
-2 -7
0 3
4 -73

f(x) = ax^2 + bx + c
f(0) = ax^2 + bx + c = 3, c = 3
f(-2) = 4a + -2b + 3 = -7
f(4) =16a + 4b + 3 = -73
4a -2b = -10 ||multiplying by 2 and adding to the 2nd EQ to eliminate b
16a + 4b = -76
24a = -96
a = -4 and b = -3 (-16 -2b = -10, -2b = 6, b = -3)

f(x) = -4x^2 - 3x + 3

Answer 5

So with f(-2), f(0), and f(4) do you plug each of those number into the equation?

Answer 6

Yes you do, @e.cociuba he shows it great

Answer 7

uhh its a girl thank you very much! :)

Answer 8

and yes @JimmiFizzle.

Answer 9

to do this problem, you need to know
1) what the equation of a parabola looks like. It is ax^2 + bx + c =0
2) you need 3 (x,y) pairs. plug these into the standard equation
3) you get 3 equations and 3 unknowns (a, b and c are the unknowns)
4) you need to be able to solve the system of equations.

Answer 10

as e.cociuba showed the 3 equations will be
c =3
4a + -2b + c = -7
16a + 4b + c = -73

Answer 11

@StudyBlu

Answer 12

Thank you all very much! :) That is so helpful. @e.cociuba , @StudyBlu , @phi

Answer 13

np:)