Question

Can someone please give me a hand? /:
What is the equation, in standard form, of a parabola that models the values in the table?
x => -2, 0, 4
f(x) => 4, -6, 70

a) y=3x^2+4x-6
b) y=4x^2+3x-6
c) y=6x^2+3x-4
d) y=-4x^2-3x+6

Any help would be amazingly helpful!

Answer 1

@satellite73 ? @Hero ?

Answer 2

@phi ? Anybody?

Answer 3

Plug in the values

Answer 4

How?

Answer 5

x => -2, 0, 4
f(x) => 4, -6, 70

this table tells that when x is -2 you should get 4 when you use the equation

I would start with x=0 (because 0 makes the arithmetic easy)

what is f(0) in each of the choices A,B,C, and D ?
f(0) is short-hand for : replace x with 0 in the equation


a) y=3x^2+4x-6
b) y=4x^2+3x-6
c) y=6x^2+3x-4
d) y=-4x^2-3x+6

I'll do the first one a) y = 3*0^2 + 4*0 - 6
what is 0^2 (btw, 0^2 is short for 0*0) ? 0*0 is 0 and 3*0*0 is still 0
for the 2nd term 4*0 is ??? yes, 0
we have y= 0+0-6 = -6
so (a) could be the equation. But check the others.

what do you get?

Answer 6

b) y=-6

Answer 7

c) y=-4

Answer 8

d) y=6

Answer 9

yes, and d) gives y = +6

the table
x => -2, 0, 4
f(x) => 4, -6, 70

says f(0) should be -6. so it looks like it's either (a) or (b)

I would check x= -2 in (a) and in (b)

what is f(-2) using a) y=3x^2+4x-6

Answer 10

22?

Answer 11

no, let's do it in small steps. First, replace x with -2 (negative numbers are more tricky)
y=3x^2+4x-6

replace x with -2:
y = 3*(-2)^2 + 4*(-2) -6

is this what you started with ?

Answer 12

Yes

Answer 13

OK, what do you get for
3*(-2)^2 ? remember this means 3* -2 * -2

Answer 14

12?

Answer 15

yes -2*-2 is 4 (two negatives make a positive when multiplying)
and 3*4 is 12
so we have

y = 12 + 4*(-2) -6

can you finish ?

Answer 16

y=12-8-6
y=-2?

Answer 17

yes, and notice that the table says

x => -2, 0, 4
f(x) => 4, -6, 70

we want to get 4, but we got -2. so (a) is out. that leaves (b) as the answer.
If this were a test and you were short of time, I would go with (b). But if you have time,
check (b)

b) y=4x^2+3x-6
what is f(-2) with this equation ?

Answer 18

y=4(-2)^2+3(-2)-6
y=16-6-6
y=4 ???

Answer 19

yes looks good, 16-6 is 10 and 10-6 is 4
so (b) works. If we were gung-ho we could check f(4) and see that it gives 70
I would do that if you need the practice.

Answer 20

Ok! Thank you so much!!!

Answer 21

yw