The parabola y=x^2
How can that equation be changed to shift the parabola three units to the left and five units down
vertex was at (0,0)
now at (-5,-3)
(y+3) = (x+5)^2
y + 3 = x^2 + 10 x + 25
y = x^2 + 10 x + 22
Where did the 10 come from ? 3^2 is 9
To shift the parabola three units to the left, you need to replace "x" with "(x+3)" in the equation. This effectively moves the entire parabola three units to the left.
To shift the parabola five units down, you need to subtract 5 from the equation. This shift affects the y-coordinate of all the points on the parabola, causing it to move downward by five units.
So, to shift the parabola y = x^2 three units to the left and five units down, you can use the equation y = (x+3)^2 - 5.