Question

Determine whether the parabola x = y2 + 3 opens up, down, left, or right.



up



down



left



right

will fan and give medal

Answer 1

@ReneeShumpert help answer

Answer 2

can someone help me please

Answer 3

@Dedi can you help me

Answer 4

@SolomonZelman could you help me

Answer 5

ok, at first there are two forms of parabolas.

(1) \(\large\color{black}{ \displaystyle {\rm y}=\color{blue}{a}{\rm x}^2+\color{blue}{b}{\rm x}+\color{blue}{c} }\)
a parabola that opens up or down

(2) \(\large\color{black}{ \displaystyle {\rm x}=\color{blue}{a}{\rm y}^2+\color{blue}{b}{\rm y}+\color{blue}{c} }\)
a parabola that opens left or right


\(\large\color{black}{ \displaystyle \color{blue}{a}}\) , \(\large\color{black}{ \displaystyle \color{blue}{b}}\) , \(\large\color{black}{ \displaystyle \text{&}}\) \(\large\color{black}{ \displaystyle \color{blue}{c}}\) can each be any real number, but with one exception that \(\large\color{black}{ \displaystyle \color{blue}{a}\ne0}\)

Answer 6

if you don't know what "real number" means, ask.

Answer 7

I will give you some examples of form (1) and form (2), okay ?

Answer 8

okay

Answer 9

Form (1), Example (1)
\(\large\color{black}{ \displaystyle {\rm y}={\rm x}^2-{\rm x}+2 }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=1 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=-1 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=2 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Form (1), Example (2)
\(\large\color{black}{ \displaystyle {\rm y}=-0.4{\tiny~}{\rm x}^2-3{\rm x} }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=-0.4 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=-3 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=0 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Form (1), Example (3)
\(\large\color{black}{ \displaystyle {\rm y}=2{\tiny~}{\rm x}^2+8 }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=2 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=0 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=8 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Form (1), Example (4)
\(\large\color{black}{ \displaystyle {\rm y}=-12.2{\tiny~}{\rm x}^2 }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=-12.2 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=0 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=0 }\)

Answer 10

this is a list of some examples of form (1), now I will post from (2) examples, and you read this while I am typing.

Answer 11

Form (2), Example (1)
\(\large\color{black}{ \displaystyle {\rm x}=-{\rm y}^2+{\rm y}-3 }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=-1 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=1 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=-3 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Form (2), Example (2)
\(\large\color{black}{ \displaystyle {\rm x}=5.2{\tiny~}{\rm y}^2-4{\rm y} }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=5.2 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=-4 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=0 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Form (2), Example (3)
\(\large\color{black}{ \displaystyle {\rm x}=6{\rm y}^2-9 }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=6 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=0 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=-9 }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Form (2), Example (4)
\(\large\color{black}{ \displaystyle {\rm x}=200{\tiny~}{\rm y}^2 }\)

In this case
\(\large\color{black}{ \displaystyle \color{blue}{a}=200 }\)
\(\large\color{black}{ \displaystyle \color{blue}{b}=0 }\)
\(\large\color{black}{ \displaystyle \color{blue}{c}=0 }\)

Answer 12

when you are done processing form (1) and form (2), tell me which form does
\(\large\color{black}{ \displaystyle {\rm x}={\rm y}^2+3 }\) belong to?

Answer 13

a=1
b=0
c=3

Answer 14

yes, and is it form(1) or form(2) ?

Answer 15

(my very first post tells you the form(1) and form(2) )

Answer 16

form 2 ex:3

Answer 17

yes, form (2)
(doesn't matter which example they are)

Answer 18

And now a new rule I am going to post (a last rule you need for this question)

Answer 19

For any form (1) parabola

\(\large\color{black}{ \displaystyle {\rm y}=\color{blue}{a} {\tiny~}{\rm x}^2+\color{blue}{b} {\tiny~}{\rm x}+\color{blue}{c} }\)

when \(\large\color{black}{ \displaystyle \color{blue}{a} >0 }\) (when a is greater than 0, that is: any positive number)
then, the parabola is opening UP

when \(\large\color{black}{ \displaystyle \color{blue}{a} <0 }\) (when a is less than 0 that is: any negative number)
then, the parabola is opening DOWN

\(\large\color{black}{ \displaystyle ( }\)there is NO case when \(\large\color{black}{ \displaystyle \color{blue}{a} =0 }\) , we have already established that, because then your graph is a line - not parabola.\(\large\color{black}{ \displaystyle ) }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

For any form (2) parabola

\(\large\color{black}{ \displaystyle {\rm x}=\color{blue}{a} {\tiny~}{\rm y}^2+\color{blue}{b} {\tiny~}{\rm y}+\color{blue}{c} }\)

when \(\large\color{black}{ \displaystyle \color{blue}{a} >0 }\) (when a is greater than 0, that is: any positive number)
then, the parabola is opening to the RIGHT

when \(\large\color{black}{ \displaystyle \color{blue}{a} <0 }\) (when a is less than 0 that is: any negative number)
then, the parabola is opening to the LEFT

\(\large\color{black}{ \displaystyle ( }\)there is NO case when \(\large\color{black}{ \displaystyle \color{blue}{a} =0 }\) , we have already established that, because then your graph is a line - not parabola.\(\large\color{black}{ \displaystyle ) }\)

Answer 20

so the parabola in in this problem opens to the right

Answer 21

yes

Answer 22

\(\large\color{black}{ \displaystyle {\rm x}={\tiny~}{\rm y}^2+3 }\)

\(\large\color{black}{ \displaystyle \Downarrow ~\Downarrow~ \Downarrow ~\Downarrow ~ \Downarrow ~\Downarrow~ \Downarrow ~\Downarrow }\)

\(\large\color{black}{ \displaystyle {\rm x}=\color{blue}{(1)} {\tiny~}{\rm y}^2+\color{blue}{(0)} {\tiny~}{\rm y}+\color{blue}{3} }\)

\(\large\color{black}{ \displaystyle \color{blue}{a} =1 }\) , and that means that \(\large\color{black}{ \displaystyle \color{blue}{a} >0 }\), therefore the parabola opens to the right

Answer 23

thanks for the help @SolomonZelman