Quadratic Transformation STAAR Algebra

The graph of f(x)= x² was transformed to create the graph of g(x) = (x - 7.5)². Which of these describes the transformation?

• A horizontal shift to the right 7.5 units

• A horizontal shift to the left 7.5 units

• A vertical shift down 56.25 units

• A vertical shift up 56.25 units

A projectile is launched into the air from the ground. The table shows the height of the projectile, h(t), at different times. Based on the table, which function can best be used to model this situation?

• h(t)= 99t² + 858

• h(t)= -4.9t² + 295t + 0.6

• h(t)= -4.9t² +295t + 2

• h(t)= 99t² + 1,470.3

If p(x) = 5(x² + 1) + 16, what is the value of p(11)?

• 690

• 736

• 622

• 626

f(x) = x² is transformed to create the graph g(x) = -f(x) + 3. Which statement below describes this transformation?

• reflection over the y axis and vertex shifts right 3 units

• reflection over the x axis and vertex shifts left 3 units

• reflection over the y axis and vertex shifts up 3 units

• reflection over the x axis and vertex shifts up 3 units

The graph of a quadratic function f is shown and the vertex is labeled with its coordinates.  If g(x) = f(x - 1) + 2, what is the minimum value of g?

* The minimum value of g is ​ (a)   because the minimum value of f is ​ (b)   and the graph of g is shifted ​ (c)   from the graph of f by ​ ​ (d)   .​

• 6

• 4

• up

• 2

• 1

• 3

• 5

• down

• left

• right

• Reflection over x-axis

• None of these

Transform the quadratic parent function to show that there is a vertical translation up 4 units, a horizontal translation left 2 units, and vertical reflection.

(Make sure one of the points is on the vertex, and the other a zero.)

Match the equation to its description.

• Reflected over x-axis and shifted up 4

• Reflected over x-axis and shifted down 4

• Reflected over x-axis and shifted right 4

• Reflected over x-axis and shifted left 4

The graph of a transformed squaring function is shown below. Which equation and description best describes the graph? Select the equation ​ (a)   and description ​ (b)  

• neither even nor odd function

• even function

• odd function

The graph of a transformed squaring function is shown below. Which equation and description best describes the graph? Select the equation ​ (a)   and description ​ (b)  

• neither even nor odd function

• even function

• odd function