Find equation from table

[craggy flame]

How do u know that function is quadratic?

[fathom nest]

because there is not a constant 1st difference

[craggy flame]

I don't get it

[fathom nest]

the first difference in Y is changing a lot, it doesnt stay the same number

if it were the same number on the first diference, it would be linear

[craggy flame]

Okay but why not cubic or smth else?

[fathom nest]

i dont know that much so i dont know 😭

i just know that in a table if the first difference is constant, the equation will be linear

[craggy flame]

I don't know either😭😭

[dawn mist]

well if youre assuming its a quadratic then we can let it take the form
ax^2 + bx + c = y
when x = 0 we know y = 2 from the table, so that means c = 2
so now we have
ax^2 + bx + 2 = y
plug in something like x=-1 y=16 we get
a - b + 2 = 16
so a-b = 14
then you try out another value like x = 1 y = 2
you get
a + b + 2 = -2
so
a+b = -4

so now you have a system of equations
a+b = -4
a-b = 14
solve it and plug in the values you get for b and c to get the final solution

let me know if you need help solving the system of equations

hint:add both equations up to solve for a

[fathom nest]

i got b = -9

is that wrong

because according to my teacher a = the second difference divided by 2

[dawn mist]

no i think its correct
lets go through it step by step

a+b = -4
a-b = 14

add both equations

a = 10

mb i mean

2a = 10

so a = 5

plug that into the first equation
5 + b = -4
so b should equal -9

so the equation should theoretically be 5x^2 - 9x + 2

[fathom nest]

okay thank you

[dawn mist]

plugging in -1 does give 16

plugging in 0 does give 2

plugging in 1 does give -2

plugging in 2 does give 4

plugging in 3 does give 20

and lastly plugging in 4 does give 46

so yeah im pretty sure it is correct

[dawn mist]

youre welcome