What is the equation, in standard form, of a parabola that models the values in the tables
x: -2,0,4
f(x): 1,5,-59

- anonymous

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- triciaal

|dw:1444365550534:dw|

- triciaal

suggest substitute the values for (x,y) and solve the simultaneous equations to get a,b,c

- anonymous

Can you explain how to do this

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- triciaal

substitute means replace now read my response again.

- anonymous

I understand that but once i replace 1=a(-2)^2+b(-2)+c what do i do from there

- triciaal

for each set

- triciaal

do you know how to solve simultaneous equations? there are about 4 methods

- anonymous

no i dont

- triciaal

ok I will work with you
what are the 3 equations?

- triciaal

this is even simplier than i thought
do you see C = 5?

- anonymous

i guess

- triciaal

no! if you have questions make sure you ask. it is very important for you to understand.

- triciaal

what are the equations when you substitute the x and y values given?

- anonymous

doesnt f(x) mean y?

- triciaal

yes

- triciaal

function of x

- anonymous

so you make 3 equations and plug 1 x in for each?

- triciaal

|dw:1444366987783:dw|

- triciaal

y = f(x) = ax^2 + bx + c

- triciaal

you did the first one correctly when x = -2
do the same process when x = 0 and again when x - 4

- anonymous

ok so what do i do now that i have the 3 equations

- triciaal

show what you have did you get C = 5?

- anonymous

i dont understand how u got c=5

- triciaal

did you do the substitutions?

- anonymous

yes i got 5=a(0)^2+b(0)+c

- triciaal

|dw:1444367515071:dw|

- triciaal

remember zero times anything is zero

- triciaal

show the 3rd one.

- anonymous

-59=a(4)^2+b(4)+c

- triciaal

and we can replace C with 5

- triciaal

also for the first one C = 5

- triciaal

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- triciaal

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- anonymous

what happened to -59?

- triciaal

|dw:1444368144737:dw|

- triciaal

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- triciaal

when you have an equation whatever you do to one side also do to the other to maintain the balance .
always group like terms to simplify

- triciaal

always factor when you can to use smaller numbers .

- triciaal

by the way notice we had equations with 3 unknown we are using substitution to solve. we had the value for c and substituted in the others. we found the expressions for b and set them equal. this gave the linear equation (one unknown) and we solve for a.

- triciaal

now that we have a,b and c we can write the general equation for f(x)

- triciaal

please review and ask any questions if you need to clear anything up. I am short on time but you need to be able to do the problem on your own.

- anonymous

i think i got it from here thank you

- triciaal

yeah we are at the end you only have to write the equation.

- triciaal

my question is do you clearly understand all what I did?

- anonymous

Yes i do

- triciaal

great!!
review and keep practicing
math is very easy with practice.

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