Quadratic transformation rules

Which transformation maps the graph of

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

• a vertical translation shifting f(x) 4 units up

• a horizontal compression by a factor of 4

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

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

Pablo throws a ball with a path of
h = -5(t - 2)².
Maria throws a ball with a path of
h = -5(t - 2)² + 10.
Which description is reasonable for the difference in the two equations?

• Maria throws the ball 10 times harder than Pablo does.
• Maria starts her ball at a height 10 feet higher than Pablo does.
• Pablo throws the ball 10 times harder than Maria does.
• Pablo starts his ball at a height 10 feet higher than Maria does.

Which description of the transformation of the graph of f(x) = x² to the graph of

g(x) = (3x)² + 2 is true?

• a horizontal compression by a factor of 1/3 with translation up two units

• a horizontal stretch by a factor of three with a translation right two units

• a vertical stretch by a factor of 3 with translation two units to the right

• a vertical compression by a factor of 1/3 with translation two units up

Describe the transformation on f(x) = x².

f(x) + 7

moved ​ (a)   7

• up
• down
• left
• right

Given the equation for this parabola: y = −(x − 4)2 − 3, does this parabola have a maximum or minimum value? (a)  

• Maximum
• Minimum

Tags

CCSS.HSF-IF.C.7A

How did we transform from the parent function f(x) = x²?

-1/2f(x - 1)² + 3

• reflection over x-axis, vertical compression by a factor of 1/2, horizontal shift right one, vertical shift up three

• vertical compression by a factor of 1/2, horizontal shift left one, vertical shift up three

• reflection over the x-axis, horizontal shift right one, vertical shift down three

• no changes were made to y = x²

How did we transform from y=x²?

-3f(x²)

• reflection over y-axis and vertical stretch

• reflection over x-axis and vertical stretch

• reflection over x-axis and horizontal compression

• reflection over y-axis and horizontal compression

If the function f(x) = x² is changed so that a new function is created, 5f(x), how does the new graph compare to f(x)?

• The graph appears wider than the graph of f(x)

• The graph appears narrower than the graph of f(x)

• The graph is shifted 5 units up above f(x)

• The graph of is shifted 5 units down below f(x)

How does the function g(x) = -x² compare the the parent function f(x)?

• The new function g(x) is reflected vertically across the x-axis

• The new function g(x) is reflected horizontally across the y-axis

• The new function g(x) has all the x-values multiplied by a -1

• The new function g(x) has been shifted 1 unit down

Which of the following shows a vertical compression of the parent function?

• 5/2f(x)²

• 3/5f(x)²

• f(4x)²

• f(3/5x)²