Transformation of Quadratic Functions

​Transformations of Quadratic Functions

Dr. Tom Giles

Multiple Choice

What are the transformations?
y = (x - 2)² + 4

• shift 2 units right
  shift 4 units up
• shift 2 units left
  shift 4 units up
• shift 2 units right
  shift 4 units down
• shift 2 units left
  shift 4 units up

Multiple Choice

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

• Minimum value, because the a value is positive
• Maximum value, because the b value is positive
• Maximum value, because the a value is positive
• Minimum value, because the c value is negative

Multiple Choice

If the blue is f(x) = x² , the red must be:

• g(x) = (x + 3)²
• g(x) = (x - 3)²
• g(x)= x² + 3
• g(x) = x² - 2

Multiple Choice

How did we transform from the parent function?
y = x² + 2

• horizontal shift up
• vertical shift up
• horizontal shift down
• vertical shift down

Multiple Choice

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

• left 3
• right 3
• left 5
• right 5

Multiple Choice

What are the green dots called?

• axis of symmetry
• vertex
• parabola
• roots or x-intercepts

Multiple Choice

Which of the following does NOT contain a REFLECTION of y = x²?

• y = -2(x + 5)² + 3
• y = (-3x + 5)² + 3
• y = (1/2) (x + 5)² + 3
• y = -x² + 3

Multiple Choice

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

• a reflection across the line x = -4
• 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

Multiple Choice

How does the graph of f(x) = (x + 3)² + 5 compare to the graph of
g(x) = (x - 1)² - 4. {Hint: Compare their vertexes.}

• f(x) is shifted 4 left and 9 up from g(x)
• f(x) is shifted 4 to the right and 9 down from g(x)
• f(x) is shifted 3 left and 5 up from g(x)
• f(x) is shifted 4 left and 9 down from g(x)

Multiple Choice

What is vertex form of a quadratic function

• ax² + bx + c
• a(x - h)² + k
• y - y₁ = m(x - x₁)
• Ax + By = C

Multiple Choice

Does the following function have a maximum or a minimum
f(x) = -2(x+3)² - 5

• Maximum
• Minimum

Multiple Choice

What is the y-intercept of the following function?
f(x) = -2x² + 3x - 7

• (0, -2)
• (0, 3)
• (0, -7)
• (0, 7)

Multiple Choice

The standard form of a quadratic function is:

• ax² + bx + c
• a(x - h)² + k
• y - y₁ = m(x - x₁)
• Ax + By = C

Multiple Choice

If a is negative in the function, which way does the parabola 

• up
• down
• left
• right

Multiple Choice

Does the following function open up or down 
1/2(x + 2)² - 3

• up
• down
• left
• right

Multiple Choice

The quadratic parent function is

• y = x
• f(x) = x
• f(x) = x²
• y = √x

Multiple Choice

y = (x + 2)² + 9
This graph shifts... 

• Left 2, down 9
• Left 2, up 9 
• Right 2, up 9
• Right 2, down 9