Quadratic Functions - Transformations

What translations occur from the parent function to create the graph of f(x) = (x + 4)² - 7?

• left 7 & down 4

• left 4 & down 7

• right 4 & up 7

• right 4 & down 7

What is the equation of the parabola shown?

• g(x) = - (x - 1)²

• g(x) = - (x + 1)²

• g(x) = (x - 1)²

• g(x) = - x² + 1

Tags

CCSS.HSF-IF.C.7A

Order the equations from widest to narrowest.

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The graph of f(x) is translated up 3 and right 8, resulting in the graph of g(x). Identify g(x) in terms of the translations performed to f(x):

• g(x) = f(x + 8) + 3

• g(x) = f(x + 3) + 8

• g(x) = f(x - 8) + 3

• g(x) = f(x - 3) + 8

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

Given f(x) = (x + 6)² - 2 , how did f(x) transform from the parent function?

• Horizontal shift left 6, vertical shift up 2

• Horizontal shift left 6, vertical shift down 2

• Horizontal shift right 6, vertical shift down 2

• Horizontal shift right 6, vertical shift up 2

If the blue graph is f(x )= x² , the equation for the red graph must be . . .

• g(x) = (x + 3)²

• g(x) = (x - 3)²

• g(x) = x² + 3

• g(x) = x² - 2

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 quadratic function would be the narrowest?