math helpp

Question

if a parabola y=x^2 is shifted from the vertex position of (0,0) to a new vertex position of (10,-20), the new equation for the parabola will be:

Answer 1

The x coordinates changes from x=0 to x=10.  This is a horizontal shift 10 units to the right from the origin. The equation becomes

 

y = (x - 10)²

 

The y coordinate changes from y=0 to y=-20.  This is a vertical shift 20 units down from the origin.  The equation along with the horizontal shift is

 

y = (x - 10)² - 20

 

Expand this out to get the function in standard form.

 

y = (x² - 20x + 100) - 20

 

y = x² - 20x + 80

Answer 2

Parabola  y = x^2 is shifted from (0,0) to (10, -20).

 

Replace x with (x-10) to make the x shift.

Replace y with (y - [-20]) to make the y shift. ie (y + 20)

 

The equation becomes:

 

(y + 20) = (x-10)^2

 

Check:

if x=10 then the right hand side is 0. Therefore the left hand side is 0. Therefore y = -20.

 

simplifying in small steps:

(y + 20) = (x-10)^2

y + 20 = (x-10)^2

y = (x-10)^2 - 20

y = x^2 - 20x + 100 - 20

y = x^2 - 20x + 80

 

check again: if x= 10

y = 10^2 - 20x10 + 80

y = 100 - 200 + 80 

y= -20

 

 

Answer 3

y = (x - h)² + k, is the equation of a parabola with vertex (h, k)

 

y = (x - 10)² - 20