Question

thanks

Answer 1

@phi

Answer 2

to graph
\[ y= -2x^2 +3 \]

do this: if x is 0 (which means replace the x in the equation with the number 0) what do you get ?

Answer 3

3?

Answer 4

@phi

Answer 5

yes 2 * 0^2 +3 is the same as
2*0*0 + 3
or
0 + 3
or 3

that means (0,3) is a point on the curve. Can you find that point on the graphs ?

Answer 6

graph (a) goes through the point (0,3)
what other graph goes through (0,3) ?

Answer 7

we don't know yet.

but we have to make sure you know where point (0,3) is on a graph
it is marked here

Answer 8

yes i know where (0, 3) is

Answer 9

and we have narrowed it down to two graphs that go through (0,3)
let's try to find another point on the graph. let x=1 in the equation

\[ y= -2x^2 +3 \]
what is y ?

Answer 10

7

Answer 11

replace the x with 1 in
\[ y= -2x^2 +3 \]

Answer 12

erase the "x" and put a 1 in its place

Answer 13

sorry i ment to

Answer 14

\[ 1^2\]
means 1*1 (1 multiplied by itself two times) it is not 1*2

try again

Answer 15

also, be careful. the equation is
\[ y= -2x^2 +3 \]

Answer 16

ok so its

Answer 17

yes, that is good arithmetic. BUT you used the wrong equation
it is supposed to be -2 in front of the 1^2

Answer 18

i sometimes get confused with the exponet

Answer 19

wait why is it -2

Answer 20

@phi

Answer 21

yes. and all the work means when x =1 then y = 1
so (1,1) is a point on the curve.

Answer 22

which graphs go through the point (1,1) ?

Answer 23

a?

Answer 24

what do you mean by go through?

Answer 25

is it not a?

Answer 26

Goes through means the point (1,1) lies on the curve.
See the attached file.

Answer 27

thats why i said its a

Answer 28

notice that only graph in (a) goes through the red circle (at point (1,1) )

Answer 29

yeah

Answer 30

Yes, that is a good reason to pick graph (a).

I was trying to answer "what do you mean by go through?"

I hope it is clear what that means. All the graphs except the first one do NOT go through the red dot.

Answer 31

no i thought through at first ment something else then i knew so the answer is a

Answer 32

one question though how did you know to use 0 and then 1 as x?

Answer 33

??

Answer 34

Here is the idea:
you have an equation
\[ y= -2x^2 +3 \]
for *every* x you can think of , you can put it into the equation and figure out what y is
that means you get (x,y) pair that you can plot. the graph is a picture of all those pairs.

If we are looking at a bunch of graphs, we want to know which of the graphs matches our equation. So the idea is , let's use the equation to find (x,y) pairs and see if the point is on the graph.

to find y, I want to make the arithmetic *easy* x=0 and x=1 are easy
we could have picked x= ⅓ (but that would be harder to do... and harder to read on the graph)

so the answer to
** how did you know to use 0 and then 1 as x?**
is x=0 and x=1 are the easiest numbers I can think of.

Answer 35

oh ok

Answer 36

do you mind helping on another one?

Answer 37

if you make it a new post.

Answer 38

ok