Question

True or False
In a quadratic function written in the vertex form y= a (x-h)^2+k, an increase in the value of h move the parabola to the right of the cartesian plane

Answer 1

remember (h, k) is the vertex

Answer 2

tell me if I am not clear with an "@" thing

Answer 3

i dont get it

Answer 4

one second.

Answer 5

sorry you can't read that, I will write those words down here.

Answer 6

I'm thinking that its false right?

Answer 7

Compare:

\(y=x^2\) (h=0)

to

\(y=(x-1)^2\) (h=1)

What happens to the position of the parabola in the plane?

Answer 8

Remember what h is: it is the x-coordinate of the vertex. So if you increase that and don't change anything else, what happens to the parabola?

Answer 9

the parabola goes upward

Answer 10

if you increase the \(\Huge \color{red} {\text{x-coordinate}}\) of the vertex????

Answer 11

Where is the point (0,0) vs. the point (5,0)?

Answer 12

the parabola would go downward @DebbieG right?

Answer 13

Where is the point (5,0) compared to the point (0,0)?

Is (5,0) directly above, below, to the right or to the left of (0,0)?

Answer 14

to the right

Answer 15

im confuse

Answer 16

ok, GOOD. So when you increase the x-coordinate of a point, that point moves to the right.

Now apply that to your problem. Do you know how to get the coordinates of the vertex, from the vertex form?

If \(\Large y= a (x-h)^2+k\) then WHAT is the vertex?

Answer 17

if \(\Large y= (x-1)^2+3\) then what is the vertex?

Answer 18

yes i know how to get the coordinates

Answer 19

OK, then what happens if you INCREASE h?

Answer 20

What is the vertex of: \(\Large y= (x-1)^2+3\)

vs.

What is the vertex of: \(\Large y= (x-2)^2+3\)

In the 2nd one, I've INCREASED h from 1 to 2. What happened to the vertex? where did it go?

Answer 21

1,3 is the coordinates

Answer 22

it also increases its value

Answer 23

I don't know what "it also increases its value" means. A vertex doesn't have a "value". It's coordinates do.

So the question I'm asking is, what HAPPENS to the vertex, e.g., where does it go, as I increased h from 1 to 2.....

did the vertex (and hence, the graph of the parabola) move to the right, the left, up or down?

Answer 24

to the right

Answer 25

You are correct that (1, 3) is the vertex in the first equation. What is the vertex in the 2nd equation? and where is that point, relative to (1, 3)?

CORRECT. So an increase in h, moved the parabola...... to the right! :)

Answer 26

so the answer is true?

Answer 27

What do you think? :)

Answer 28

We just showed that, didn't we? ;)

Answer 29

thanks

Answer 30

You're welcome. :)