Answer:
a) y = (x - 3)²
b) y = x² - 4
c) y = (x + 2)²
d) y = x² + 5
e) y = (x + 6)² - 7
f) y = (x - 2)² + 5
Step-by-step explanation:
Parent equation: y = x²
Transformed equation: y = (x - h)² + k
h translates the parabola horizontally
If h > 0 then the translation is h units to the right.
If h < 0 then the translation is h units to the left.
If h = 0 then there is no horizontal translation.
k translates the parabola vertically
If k > 0 then the translation is k units up.
If k < 0 then the translation is k units down.
If k = 0 then there is no vertical translation.
a) The parabola moves 3 units to the right:
⇒ y = (x - 3)² + 0
⇒ y = (x - 3)²
b) The parabola moves 4 units down:
⇒ y = (x - 0)² - 4
⇒ y = x² - 4
c) The parabola moves 2 units left:
⇒ y = (x + 2)² + 0
⇒ y = (x + 2)²
d) The parabola moves 5 units up:
⇒ y = (x - 0)² + 5
⇒ y = x² + 5
e) The parabola moves 7 units down and 6 units left:
⇒ y = (x + 6)² - 7
f) The parabola moves 2 units right and 5 units up:
⇒ y = (x - 2)² + 5
