I. The parent function of a quadratic Which of these are characteristics of the parent function of a quadratic equation? I. The parent function of a quadratic equation has the vertex at (0, 0). II. The parent function of a quadratic equation opens downward. III. The parent function of a quadratic equation has the y-axis as its line of symmetry. A I and II only B I and III only C II and III only D I, II, and III A.2A

Which equation is the parent function of the graph represented below? A.2A

The quadratic parent function can be described by the equation: y = x2 Sketch the graph. A.2A

Which parent function describes the graph of a function that passes through the points (2, 4), (-2, 4), and (0, 0)? Justify your answer. A.2A

What type of parent function is modeled in the graph? A Absolute Value The graph below models the relationship between the time, in seconds, when a baseball is thrown straight up in the air and its height, in feet. What type of parent function is modeled in the graph? A Absolute Value B Exponential C Linear D Quadratic A.2A

f(x) = 2x2 - 32 represents the profit/loss of a manufacturing company. How must the domain of f(x) be restricted if the profit/loss function is to be positive? A.9A

a) Do all quadratic functions have the same domain? The quadratic function f(x) = x2 has a domain of all reals and a range y ≥ 0.  a) Do all quadratic functions have the same domain?   b) Do all quadratic functions have the same range? A.9A

Apex Manufacturing Company models their revenue for a particular product with the function R = $100 - x2 where x represents the number of days that it takes to produce their product.   A. Explain how the president of the company knows that if production exceeds 10 days the company will lose money. B. Determine whether the domain in this situation is revenue or number of days. A.9A

A.9B

A.9B

How does the graph of Equation 2 differ from the graph of Equation 1? These equations are graphed on a coordinate graph. Equation 1: y = x2 Equation 2: y = 5x2 How does the graph of Equation 2 differ from the graph of Equation 1? A The vertex is 5 units higher. B The vertex is 5 units lower. C It is narrower. D It is wider. A.9B

A. Complete the four tables below. Some In this problem, the goal is to look at the relationship between the graph of y = x2 and y = ax2 when a > 0 . A. Complete the four tables below. Some cells may have more than one answer. B. For a = 2, 3, 4, which factor does the graph of y = ax2 change in each of the tables? C. If a < 0 , explain what happens to the graphs of the tables in part A. A.9B

The graphs below represent functions of the form y = ax2. In which of the following graphs does a have the smallest value? largest value? positive value? negative value? A.9B

The graph of the function y = x2 − 3 is shown below. If the graph of the original function is shifted 5 units up, which of the following equations best represents the translation of each point on the curve? F y = x2 + 5 G y = x2 + 2 H y = x2 − 2 J y = x2 − 8 A.9C

A The graph would shift 3 units up. How would the graph of the function y = x2 + 4 be affected if the function were changed to y = x2 + 1? A The graph would shift 3 units up. B The graph would shift 3 units down. C The graph would shift 3 units to the right. D The graph would shift 3 units to the left. A.9C

Which graph shows a function y = x2 + c … when c < −1? … when c > 0 … when c = 0 A.9C

What is the effect on the graph of the equation y = x2 + 1 when it is changed to y = x2 + 5? A The slope of the graph changes. B The curve translates in the positive x direction. C The graph is congruent, and the vertex of the graph moves up the y-axis. D The graph narrows. A.9C

The graph of y = 11x2 + c is a parabola with a vertex at the origin The graph of y = 11x2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c? A c > 0 B c < 0 C c = 0 D c = 11 A.9C

A The rocket reached its maximum height after 2.5 seconds. The graph below shows h, the height in meters of a model rocket, versus t, the time in seconds after the rocket is launched. From the graph, what conclusion can be made about the flight of the rocket? A The rocket reached its maximum height after 2.5 seconds. B At 0 seconds the rocket was 2 meters off the ground. C The height of the rocket was 0 meters when it was launched. D The rocket was in flight for 5 seconds. A.9D

A.9D

A.9D

A.9D

The function h = 96t – 16t2 , represents h, the height of a ball thrown into the air, or t seconds. If a ball is thrown into the air with an initial velocity of 96 feet per second, what would be the maximum height? A 80 feet B 128 feet C 144 feet D 154 feet A.9D

A. What is the height of the ball after three seconds? The equation below represents h, the height of a ball thrown upward, and the time, t, it takes to hit the ground. h = 100t - t2 A. What is the height of the ball after three seconds? B. In the table below, complete the heights for the given seconds. A.9D

A.9D

A.9D