Step-by-step explanation:
The general form for a quadratic or cubic equation is:
y = a (x − h)ⁿ + k
If |a| is between 0 and 1, it's a vertical shrink. If |a| is greater than 1, it's a vertical stretch. If a is negative, there's a reflection over the x-axis.
h is the horizontal translation. If h is positive, there's a translation to the right. If h is negative, there's a translation to the left. (Notice the expression in the parentheses is x − h, not x + h, so if it helps, rewrite the equation.)
k is the vertical translation. If k is positive, there's a translation up. If k is negative, there's a translation down.
f(x) = (x + 1)³ − 7
f(x) = 1 (x − -1)³ + -7
a = 1, h = -1, k = -7
This is y = x³ translated 1 unit to the left and 7 units down.
g(x) = -½ (x − 2)³
g(x) = -½ (x − 2)³ + 0
a = -½, h = 2, k = 0
This is y = x³ reflected over the x-axis, vertical shrink of ½, and translated 2 units to the right.
y = -(x − 4)³ − 2
y = -1 (x − 4)³ + -2
a = -1, h = 4, k = -2
This is y³ reflected over the x-axis, translated 4 units right and 2 units down.
