For Exercises 1 3, Choose the Graph That Describes the Transformation of F(X) = X2

Algebra 2 Name ______Review – Unit 2

For Exercises 1 – 3, choose the graph that describes the transformation of f(x) = x2.

1) g(x)  (x  4) 2 A) B) C)

2) g(x)  (x  3) 2  2 A) B) C)

3) g(x)  3(x  2)2 1 A) B) C)

Write a rule for g and identify the vertex. 2 4) Let the graph of g be a vertical shrink of 3 , followed by a translation 5 units left and 2 units down of the graph of f (x)  x 2 . Equation: ______Vertex: ______

5) Let the graph of g be a reflection in the x-axis, followed by a translation of 3 units right of the graph of f (x)  x 2 .

Equation: ______Vertex: ______In Exercises 6-9, graph the function. Label the vertex and line of symmetry.

6) f (x)  2x 2  5 7) f (x)  x 2  2x  4

Vertex: ______Vertex: ______

Line of Sym. ______Line of Sym. ______

8) f (x)  3(x  4)2  4 9) f (x)  x 2  2x 1

Vertex: ______Vertex: ______

Line of Sym. ______Line of Sym. ______

Find the maximum or minimum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing.

10) f (x)  3(x 1) 2  4 Vertex ______Line of Symmetry ______

Max or Min ______Value ______

Domain: ______Range ______Increasing ______Decreasing ______

11) f (x)  2x 2 16x  3 Vertex ______Line of Symmetry ______

Domain: ______Range ______Increasing ______Decreasing ______12) f (x)  (x  3)(x  7) Vertex ______Line of Symmetry ______

Domain: ______Range ______Increasing ______Decreasing ______

Label the x-intercepts, vertex, and axis of symmetry.

13) f (x)  (x  3)(x  3) 14) f (x)  3(x  2)(x  6) 15) f (x)  4x(x  7) x-int. ______x-int ______x-int ______vertex ______vertex ______vertex ______ax. of sym. ______ax. of sym. ______ax. of sym ______

16) The height of a bridge is given by y  .002x 2  x 105.4 , where y is the height of the bridge (in meters) and x is the number of meters from the base of the bridge.

a) How far from the base of the bridge does the maximum height occur? ______

b) What is the maximum heightof the bridge? ______

17) The table shows the height y of a dropped object ater x seconds. Time (sec) x 0 0.5 1 1.5 2 2.5 Height (ft) y 150 146 134 144 86 50

a) Use the regression feature on your calculator to find a function to model the data (round the nearest tenth).

b) What is the height of the object after 2.75 seconds?

Write the equation of the parabola in vertex form. 18) Vertex: (2, -3) and passes through (6, 4) 19) x-int of 10 and 6; passes through (11, 8)

21) Use the graph. The x and y intercepts have been plotted for you.

The x-intercepts of a parabola are (-2, 0) and (4, 0).

The y-intercept of a parabola is (0, -16).

a) If the minimum value of the parabola is -18, what is the vertex of the parabola?

b) Find the value of “a”.

c) Write the equation in vertex form.