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

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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

Mathematics
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|dw:1444365550534:dw|
suggest substitute the values for (x,y) and solve the simultaneous equations to get a,b,c
Can you explain how to do this

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substitute means replace now read my response again.
I understand that but once i replace 1=a(-2)^2+b(-2)+c what do i do from there
for each set
do you know how to solve simultaneous equations? there are about 4 methods
no i dont
ok I will work with you what are the 3 equations?
this is even simplier than i thought do you see C = 5?
i guess
no! if you have questions make sure you ask. it is very important for you to understand.
what are the equations when you substitute the x and y values given?
doesnt f(x) mean y?
yes
function of x
so you make 3 equations and plug 1 x in for each?
|dw:1444366987783:dw|
y = f(x) = ax^2 + bx + c
you did the first one correctly when x = -2 do the same process when x = 0 and again when x - 4
ok so what do i do now that i have the 3 equations
show what you have did you get C = 5?
i dont understand how u got c=5
did you do the substitutions?
yes i got 5=a(0)^2+b(0)+c
|dw:1444367515071:dw|
remember zero times anything is zero
show the 3rd one.
-59=a(4)^2+b(4)+c
and we can replace C with 5
also for the first one C = 5
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what happened to -59?
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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
always factor when you can to use smaller numbers .
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.
now that we have a,b and c we can write the general equation for f(x)
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.
i think i got it from here thank you
yeah we are at the end you only have to write the equation.
my question is do you clearly understand all what I did?
Yes i do
great!! review and keep practicing math is very easy with practice.

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