Transforming Quadratic Equations

How did we transform from the parent function? g(x) = -1/5(x - 1)² + 7 What would be the new vertex and range?

What is the equation of the quadratic function obtained from horizontally shifting the parent function 17 units left and then reflecting across the x-axis?

• f(x)= -x²-17

• f(x)= -(x-17)²

• f(x)= -(x+17)²

• f(x)= -x²+17

Match the equation to its description.

• Stretched by 4 and up 4

• Compressed by 4 and up 4

• Stretched by 4 and left 4

• Compressed by 4 and left 4

What is the vertical shift of this equation?
f(x) = -(x + 3)² - 5

• left 5

• right 5

• up 5

• down 5

Which of the following describes the transformations done to the quadratic parent function of f(x) = x²  to obtain g(x) = 2x² + 4 ?

• Vertical Stretch by a factor of 2 and vertical shift up 4 units

•  Vertical Shrink/Compress by a factor 2 and vertical shift up 4

• Vertical Stretch by a factor of 2 and horizontal shift left 4 units

• Vertical Shrink/Compress by a factor of 2 and horizontal shift right 4 units

The graph of a quadratic function f is shown and the vertex is labeled with its coordinates.  If g(x) = f(x - 1) + 2, what is the minimum value of g?

* The minimum value of g is ​ (a)   because the minimum value of f is ​ (b)   and the graph of g is shifted ​ (c)   from the graph of f by ​ ​ (d)   .​

• 6

• 4

• up

• 2

• 1

• 3

• 5

• down

• left

• right

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a reflection across the x-axis

• a reflection across the line y = -4

• a translation shifting f(x) 4 units to the left

• a translation shifting f(x) 4 units to the right

• reflected across x-axis

• horizontal shift right

• vertical shift up

• vertical

  compression

• vertical stretch

• Maximum

• Left 5

• Down 8

• vertical shrink

• Minimum

• Right 5

• Up 8

• Vertical Stretch

• No Vertical Shift