Answer: 4) shift left 1 unit & up 4 units and reflection over x-axis
5) shift down 5 & vertical shrink by a factor of 1/3
Step-by-step explanation:
The vertex form of a quadratic equation is: y = a(x - h)² + k where
- "a" is the vertical stretch (shrink if |a| < 1)
- -a is a reflection over the x-axis
- (h, k) is the vertex
- h is the horizontal shift (positive = right, negative = left)
- k is the vertical shift (positive = up, negative = down)
4) y = -(x + 1)² + 4
↓ ↓ ↓
a= -1 h= -1 k= 4
a = -1: reflection over the x-axis
h = -1: shifted left 1 unit
k = 4: shifted up 4 units
Graph:
Plot the vertex (h, k) = (-1, 4)
a = -1 so plot down 1 right 1 --> (0, 3) and down 1 left 1 --> (-2, 3)
Draw a curve through those 3 points.
5) y = 1/3(x - 0)² - 5
↓ ↓ ↓
a= 1/3 h= 0 k= -5
a = 1/3: vertical shrink by a factor of 1/3
h = 0: no change
k = -5: shifted down 5 units
Graph:
Plot the vertex (h, k) = (0, -5)
a = 1/3 so plot up 1 right 3 --> (3, -4) and up 1 left 3 --> (-3, -4)
Draw a curve through those 3 points.
