What will the equation be if the following equation is translated 6 units left and 3 units up? Equation: f(x)=x^2

g(x) = (x+3)²

Step-by-step explanation:

You start at point ( 0,0 )

The graph of f(x) is is shifted 3 units to the left to obtain the graph of g(x)...

Here is what you do:

(x,y) > (x-3,y)

Applying the rule of the translation at the vertex of the graph of f(x)

( 0,0 ) > (0-3,0)

( 0,0 )> (-3,0)

The vertex of the graph of g(x) is the point ( -3,0 )

So the equation of g(x) would be equaled to:

g(x) = (x+3)²

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

answer: 40.95

step-by-step explanation: