USATP# 5 - Graph Transformations

The graphs represent equations of the form y = x² + c. For which graph is the value of c the greatest?

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The function shown is in the form y = x² + k. Determine the value of k.

• -1

• 0

• 1

• -½

Tags

CCSS.HSF-IF.C.7A

The function shown is in the form y = (x - h)². Determine the value of h.

• -1

• 1

• 2

• -½

Tags

CCSS.HSF-IF.C.7A

If the quadratic functions for the equations are graphed, which is the widest?

• y = x²

• y = 2x²

• y = 6x²

• y = ¼x²

Heather is going to graph y = -3x² + 3. How is the parent graph transformed?

• The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

• The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

• The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted left 3 units.

• The parent graph is reflected over the x-axis, has a vertical compression by a factor of 3 and is shifted up 3 units.

Which statement explains the difference between the graphs of f(x) = x² and g(x) = -(x² - 2)?

• The graph of f(x) is obtained by flipping g(x) over the x-axis and shifting up 2 units.

• The graph of g(x) is obtained by flipping f(x) over the x-axis and shifting up 2 units.

• The graph of f(x) is obtained by flipping g(x) over the x-axis and shifting left 2 units.

• The graph of g(x) is obtained by flipping f(x) over the x-axis and shifting left 2 units.

The function f(x) = x² is transformed to f(x) = ½(x − 2)². Which statement describes the effect(s) of the transformation on the graph of the original function?

• The parabola is narrower and shifted 2 units to the right.

• The parabola is narrower and shifted 2 units to the left.

• The parabola is wider and shifted 2 units to the right.

• The parabola is wider and shifted 2 units to the left.

The function f(x) = x² is transformed to f(x) = 0.4(x + 1)². Which statement describes the effect(s) of the transformation on the graph of the original function?

• The parabola is wider and shifted 1 unit to the left.

• The parabola is wider and shifted 1 unit to the right.

• The parabola is narrower and shifted 1 unit to the left.

• The parabola is narrower and shifted 1 unit to the right.

Quadratic functions "q" and "w" are graphed on the same coordinate grid. the vertex of the graph of "q" is 11 units below the vertex of the graph of "w". Which pair of functions could have been used to create the graphs of "q" and "w"?

• q(x) = 11x² and w(x) = x²

• q(x) = x² + 11 and w(x) = x²

• q(x) = -11x² and w(x) = x²

• q(x) = x²-11 and w(x) = x²

Function "p" is in the form y = ax² + c. If the values of "a" and "c" are both less than 0, which graph could represent "p"?

• Graph A

• Graph B

• Graph C

• Graph D

Tags

CCSS.HSF-IF.C.7A