Determine the transformation and use them to graph each quadratic function

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

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.

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: