Quadratic Functions Transformation

Order the equations from widest to narrowest.

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• 
• 
• 

Given h(x) = a⋅x²

If g(x) = 3x² and h(x) is wider than g(x), what could be the value of a?

• -4

• 4

• -3

• 2

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

• becoming wider or vertically compressed

• becoming narrower or vertically stretched

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x) in terms of f(x)?

• g(x) = f(x + 3)

• g(x) = f(x - 3)

• g(x) = f(x) + 3

• g(x) = f(x) - 2

Which equation best represents the graph?

• y = 2(x - 4)² + 5

• y = 2(x + 4)² + 5

• y = -2(x - 4)² + 5

• y = -2(x + 4)² + 5

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

• a vertical translation 4 units up

• a vertical translation 4 units down

• a horizontal translation 4 units to the left

• a horizontal translation 4 units to the right

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

• horizontal shift down and vertical shift left

• horizontal shift left and vertical shift down

• horizontal shift right and vertical shift up

• horizontal shift up and vertical shift right

What is the axis of symmetry of this parabola?

• -4

• x = -4

• x = -2

• y = -4

Identify the function graphed here.

What is the vertex of this parabola?

Hint: The highest or lowest point of the U

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)