Question

36. The function f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and down 3 units.
What is the function rule for g(x)?

Answer 1

@KyloRen

Answer 2

@nincompoop

Answer 3

Do you know how \(f(x) = x^2\) looks like?

Answer 4

yes

Answer 5

What is the coordinate \((x,y)\) of the turning point/vertex?

Answer 6

the vertex is 0,0

Answer 7

it would be 3,-3. but how can i figure out the function

Answer 8

When we shift the graph up or down the y-axis (vertically), does the y-coordinate of the vertex change?

Answer 9

of course it will

Answer 10

Okay. If the vertex starts at (0,0) (the y-value is 0) and we shift the graph down by 3 units, does the y value increase or decrease? What is the new y value?

Answer 11

decrease. the new value is 3,-3

Answer 12

Since shifting down by 3 units decreases the y value, what would you do to your function, \(y=x^2\), to show that the y value gets smaller?

Answer 13

put a - sign before it?

Answer 14

Well you just told me that moving the graph down by 3 changed the value of the y-coordinate from 0 to -3. What must we do to 0 to get to -3?

Answer 15

- 3

Answer 16

Right. Notice that the function \(y=x^2\) gives you the value of the \(y\) coordinate. If shifting the graph down by 3 units requires you to subtract the y-coordinate by 3, what must we do to the function \(y=x^2\)?

Answer 17

make it -3x^2

Answer 18

Close. Since you subtract the y-coordinate by 3, you'll also subtract the function by 3: \(y = -x^2 -3\).

Answer 19

Now consider what happens when you move the graph left or right (horizontally) -- this affects the x-coordinate. If we started at \((0,0)\) and moved to the right by 3, does the x-coordinate increase or decrease?

Answer 20

close the Q

Answer 21

before i close it

Answer 22

it would not be -3x^2; it would be x^2 -3 to shift down 3 units

Answer 23

how? @triciaal

Answer 24

A quick restart:

"The function f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule for g(x)?"

The general quadratic equation in "vertex form" is y=(x-h)^2+k.

If the vertex is at the origin, (0,0), this equation becomes y=x^2.

If the whole graph, of course including the vertex, is translated 2 units to the right, the equation becomes y=(x-2)^2+0 = (x-2)^2.

If the whole graph, incl. the vertex, is translated downward 5 units, the equation becomes y=x^2-5.

@mflow24: Please use this structure and these examples to answer the question you've posted.

Answer 25

Rewrite the given equation y=(x-h)^2 + k based upon the vertex being at (3,-3).

Answer 26

so the answer would be y=x^2? @mathmale

Answer 27

Sorry, but no. Where did you get that? The vertex is at (3,-3).

Answer 28

ok so then y=x^2-3?

Answer 29

@mathmale