Question

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

x~ -2 , 0 , 4
f(x)~ 1 , 5 , -59

Answer 1

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 2

so it will be:
a(-2)^2+b(-2)+c ?

Answer 3

f(-2) = 1
means
a(-2)^2+b(-2)+c = 1

Answer 4

we will have 3 equations so we could find a,b and c.

Answer 5

and the 2nd will be :
a(0)^2+b(0)+c=5

Answer 6

yes

Answer 7

write it after you simplify ..

Answer 8

and the 3rd will be :
a(4)^2+b(4)+c=-59

Answer 9

yes

Answer 10

so write the 3 simplified equations

Answer 11

so the 1st one simplified is a*4+b*-2+c=1 ?

Answer 12

yes which is
4a-2b+c=1

Answer 13

now what are the other 2 ?

Answer 14

the 2nd would be :
0a+0b+c=5 ?

Answer 15

which means ? what is 0a ? 0b ?

Answer 16

what ?

Answer 17

0*a is 0a which is 0 .. since it's 0 times something ..
so
0a +0b+c=5
is like
c = 5

agree?

Answer 18

agree (:

Answer 19

4a-2b+c=1
c = 5
what is the third ?

Answer 20

& the third would be:
16a+4b+c=-59

Answer 21

good
so we have system of equations :
4a-2b+c=1
c = 5
16a+4b+c=-59

Answer 22

we know from the second equation that c = 5..
can you find a and b ?

Answer 23

do i plug 5 for c in the 1st & 3rd equation?

Answer 24

yes

Answer 25

and then you left with 2 equations and 2 unknowns

Answer 26

so :
4a-2b+5=1 ?

Answer 27

this is the first

Answer 28

yes

Answer 29

can you solve 2 equations with 2 unknowns ?
find a and b ..

Answer 30

I dont know how to find a & b ?

Answer 31

@andreascott "do i plug 5 for c in the 1st & 3rd equation?"
Yes, please do ! then show your results.

Answer 32

so :
4a-2b+5=1 ?

Answer 33

what about the third ?

Answer 34

16a+4b+5=-59 ?

Answer 35

4a-2b+5=1 --> 4a - 2b = ...?

Answer 36

im confused now ?

Answer 37

we want in the left side of the equations only a,b so we want to get rid of the 5 in the left side
what the equations will look like ?

Answer 38

4a-2b ?

Answer 39

= ?

Answer 40

4a-2b = 5 ??

Answer 41

4a-2b+5=1
subtract 5 from both sides (in order to have only a and b in the left side)
4a-2b +5 -5 = 1-5
4a-2b = -4

Answer 42

can you do the same for the other equation ?

Answer 43

16a+4b+5=-59
->16a+4b = ...?

Answer 44

16a+4b+5=-59 ?
16a+4b+5 - 5 = 20 -5 ?
16a+4b = 15 ?

Answer 45

how -59 turned into 20 ?

Answer 46

i thought you did 4-2 = 1
so i did 16+4 =20 ?

Answer 47

first, 4-2 = 2
second you have to work with the original equation
which is (ill show work on the first one)
4a-2b+5=1
now i subtract 5 from both sides of the equation (the 1 was there because this is the original equation)
4a-2b +5-5= 1-5
4a-2b = -4

Answer 48

4a-2b +5 -5 = 1 -5
4a-2b = -4

Answer 49

i havent changed any thing .. just moved the 5 into the right side

Answer 50

ohhhhhhhh , i feel reallly slow . excuse me . lol im not thinking right

Answer 51

it's fine

Answer 52

im sure you done those things before

Answer 53

can you do the same for the second equation now ?

Answer 54

I have a head -ache -______-

Answer 55

16a+4b+5 -5 = -59 -5
16a+4b = -64 ?

Answer 56

good!

Answer 57

so now we have

4a-2b = -4
16a+4b = -64

in order to solve for a or for b
we can use the elimination or substitution method
have you heard about it ?

Answer 58

heard about it , but cant remember how to start it off ?

Answer 59

for example .. if we want to use the elimination method
and we want to eliminate a and solve for b first
we may multiply both sides of the first equation by 4
(so the a term will be 16a)
and then we will have :
4(4a-2b) = -4 *4
16a - 8b = -16

so we have
16a - 8b = -16
16a+4b = -64

and then we can subtract the second from the first
can you show me how you do this ?

Answer 60

plug -64 into 4a-2b = -4 ?

Answer 61

we have to subtract the second equation from the first

so we subtract the right side of the second equation from the right side of the first
and subtract the left side of the second equation from the left side of the first

Answer 62

i dont understand ?

Answer 63

16a - 8b = -16
16a+4b = -64


->

16a - 8b -(16a+4b) = -16 - (-64)

Answer 64

i kinda see . . .

Answer 65

now simplify

Answer 66

a -4b = 48 ?

Answer 67

no
show me how you did it

Answer 68

i did 16a -16a & got 0 .
then i did -8b + 4b & got -4 .
then i did -16 - ( 64) & got 48 .

Answer 69

so why i see a in your answer

Answer 70

and it is -8b-4b

Answer 71

ohhh , there is no a . my fault . so its -4b=48 ?

Answer 72

and it is -8b-4b

Answer 73

& when u simplify that its -12b ?

Answer 74

yes .

Answer 75

so what is the equation after simplification

Answer 76

-12b=48

Answer 77

what is b then?

Answer 78

i knew that , im just thinking tooo hard .

Answer 79

b=-4 ?

Answer 80

good..
so now in order to find a we plug b in one of the two equations we had .

Answer 81

4a-2(-4) = -4

Answer 82

?

Answer 83

yes so what is a ?

Answer 84

8 or 2 ?

Answer 85

there is only one answer
show me

Answer 86

4a+8=-4 ?

Answer 87

...

Answer 88

so what is a

Answer 89

idk ? 4 ?

Answer 90

4a+8=-4

isolate a ..
subtract 8 from both sides ..
its one equation with one unknown you know how to solve for a!

Answer 91

8-4a +8 = -4-8 ?

Answer 92

4a+8=-4
subtract 8 from both sides
4a +8-8 = -4-8
4a = -12
divide both sides by 4
a = -3

Answer 93

you know how to do it .. Im sure.. i guess you are tired.

Answer 94

so we found a,b and c
look at the first thing i wrote in this post and tell me what is the parabola

Answer 95

f(x) = -3x^2+-4x+5 ?

Answer 96

+-4x is like -4x

Answer 97

f(x) = -3x^2-4x+5 ?

Answer 98

yes.. a good thing to do is to check ourselves and see if we plug in the data we get the correct given data