Question

PLEASE HELP ME. I WILL MEDAL AND FAN.
1. What is the equation, in standard form, of a parabola that contains the following points? Show your work.

(–2, -20), (0, -4), (4, -20)

Answer 1

do you know the standard formula of a parabola?

Answer 2

y=ax + bx + c

Answer 3

right?

Answer 4

do you know graph end behaviours

Answer 5

close you forgot the square on the x in the first term.

Answer 6

no. i don't

Answer 7

oh yeah. i forgot. sorry.

Answer 8

how about quadratic formula

Answer 9

so it should actually be \[ax^{2}+bx+c\]

Answer 10

I don't remember the quadratic formula.

Answer 11

ok so it's saying that you have to have these three points so why not setup a system of equations. Do you know how to do so?

Answer 12

sorry no. could you walk me through it?

Answer 13

sure so for each point take the equation and plug the point into the formula. So for the point (-2,-20) plug that into y= ax^2+bx+c. Show me how you do that.

Answer 14

so it would be
20=a(-2)^2+-2b+c

Answer 15

minor mistake but it should be -20=a(-2)^2+-2b+c. ok so simplify that down.

Answer 16

oops. sorry again.

Answer 17

no problem they are just careless mistakes. Just be careful during tests.

Answer 18

y=ax^2+bx+c

Answer 19

okay.
-20=-4a+-2b+c ?

Answer 20

to find out a , b , c .....plug in the point in equation

Answer 21

hmmm...-2^2 is what?

Answer 22

plug in each point and u will get 3 equation

Answer 23

omg. its 4….

Answer 24

yup so your equation should be?

Answer 25

im so out of it….

Answer 26

-20=4a+-2b+c ?

Answer 27

yes beautiful. Ok so now keep that aside and lets move onto the next point. (0,-4). What will the equation be, if we do the same thing?

Answer 28

-4=a(0)+b(0) +c

Answer 29

simplify that down?

Answer 30

-4 = c ?

Answer 31

Nice! Alright now for the last point of (4,-20)?

Answer 32

-20=16a+4b -4
-5 = 16a +4b

Answer 33

so I agree with the first equation you posted:-20=16a+4b -4 but I don't know how you got to the next equation.

Answer 34

oh. was i supposed to simplify the first equation?

Answer 35

yes! But you did so incorrectly lol!

Answer 36

lol. sorry!!! what should i have done?

Answer 37

well tell me what you should do to simplify -20=16a+4b -4 down

Answer 38

divide -4 on both sides of the equation?

Answer 39

mmm we could do that...but why can we first just add 4 to both sides?

Answer 40

*can't

Answer 41

oh. to cancel it out?

Answer 42

yes!

Answer 43

ok. so
-16=16a+4b

Answer 44

beautiful! Now we can divide 4 on each side like you wanted

Answer 45

we could have done it at the beginning actually but this way takes less math.

Answer 46

lol okay.
-4=16a + b

Answer 47

well...16a/4 =?

Answer 48

4a

Answer 49

so your equation should be?

Answer 50

-4=4a + b

Answer 51

nice!

Answer 52

so what are the three equations that we have so far?

Answer 53

-20=4a+-2b+c
-4 = c
-4=4a + b

Answer 54

oh wait...

Answer 55

yes?

Answer 56

shouldn't i simplify the first one by plugging in the value of c?

Answer 57

yes!

Answer 58

-16=4a-2b?

Answer 59

yes!

Answer 60

so now that we've used the second equation fully. What are the two equations that we have to work with?

Answer 61

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

Answer 62

so you have an idea of how to simplify the two into 1 equation?

Answer 63

could you show me? i remember you have to somehow combine the two equations by canceling out one of the variables…i think..

Answer 64

haha that didn't come out at all...but sure, why not cancel out the equations but substracting one from another like this: do you know how to do so?

Answer 65

like multiply the bottom equation by -1...

Answer 66

or we could do it that way of isolating one variable and substituting, it's up to you,

Answer 67

which one is easier?

Answer 68

how would you do that>

Answer 69

the first way. as for how you do it. Just simply subtract like you would normally do it so what's -16 - -4? Do you see how that works?

Answer 70

okay. so then it would be:
-12=-3b?

Answer 71

beautiful!

Answer 72

simplify?

Answer 73

-4 = b?

Answer 74

well...-12/-3 is?

Answer 75

4

Answer 76

so?

Answer 77

4 = b

Answer 78

yes now we can solve for a can't we?

Answer 79

yeah. so -2=a

Answer 80

yes! so what's our entire equation?

Answer 81

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

Answer 82

where's the x for the second term?

Answer 83

oops….
y = -2x^2 + 4x + -4

Answer 84

nice! and there you go! Your answer!

Answer 85

Thank you so much! :))))

Answer 86

no problem! You did the work!

Answer 87

lol. only cos' i was guided by such a smart teacher.

Answer 88

aww thanks...but not really lol.