Name Period Date Vocabular: Define each word and give an eample.. Quadratic Function NON-CALCULATOR SECTION. Zero (of a function) 3. One-to-One Function Short Answer:. Describe how to find a quadratic inverse and how it can be verified. 5. What is the discriminant of the quadratic equation a + b + c =? Describe what it means if the discriminant is negative, positive, or zero. Review:. Find f g if f( ) = 5 and g ( ) = + 7. 7. The graph of = f( ) is reflected in the -ais, is shifted 5 units up and 3 units right. The equation of the transformation is:. Simplif: (3 )( i + 9) i Problems: **Be sure to show all work used to obtain our answer. Circle or bo in the final answer.** 9. Solve the quadratic equations b factoring. 5 = b. 9 + = c. =. Solve the quadratic equations b square roots.
5 = b. ( ) 3 + + = c. =. Solve the quadratic equation b completing the square: + =. Solve the quadratic equation b the quadratic formula: 5 + = 3. Find the discriminant and decide whether the equation has one, two or zero real solutions. + + =. Write = + 9 in verte form. Find the zeros and the verte of the function. 5. Find the inverse of each function. Graph and label the function and its inverse. State the domain and range of each function and its inverse. Determine whether the inverse is a function. f( ) = ( ) b. f( ) = 3, > - - - - - - - - - - - - - - - -. Find the inverse of the function
f ( ) ( ) 5 = + and verif it b composition. 7. 3, < f( ) = +, <, D f R f = = evaluate: f ( 3) = f () = f () =. Solve b graphing and answer the questions below. h() = 3 9 7 5 3 - -9-7 - -5 - -3 - - 3 5 7 9 - - -3 - -5 - -7-9 - = Verte: Ma or min? Direction of opening? Wider or narrower than =? Domain: Range: -intercepts: Ais of smmetr: 9. Solve the quadratic inequalities: 9 < b. 3. The ages of three famil children can be epressed as consecutive integers. The square of the age of the oungest child is more than eight times the age of the oldest child. Find the ages of the three children.. If the measure of one side of a square is increased b centimeters and the measure of the adjacent side is decreased b centimeters, the area of the resulting rectangle is 3 square centimeters. Find the measure of one side of the square.
. Write the equation for the graph: Multiple Choice Questions: Circle the best answer. 3. What are the solutions of the quadratic equation 3 5 + =? A. B. 5 + i 3 5 i 3, = C. 5 + i 3 5 i 3, = D. 5 + i 73 5 i 73 =, 5 + i 73 5 i 73 =,. Which is one of the appropriate steps in finding the solutions for + 9= when solved b completing the square? A. ( + ) = 5 C. ( ) + = 9 B. ( + ) = 9 D. ( )( ) + 9 = 5. For the scenario below, use the model h= t + vt+ h, where h = height (in feet), h = initial height (in feet), v = initial velocit (in feet per second), and t = time (in seconds). A cheerleading squad performs a stunt called a basket toss where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward, leaving her teammates hands feet above the ground with an initial vertical velocit of 5 feet per second. When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air? A. B. second C. second 9 second D. seconds
Name Period Date CALCULATOR SECTION. Old Faithful in Yellowstone Park is probabl the world s most famous geser. Old Faithful sends a stream of boiling water into the air. During the eruption, the height h (in feet) of the water t seconds after being forced out of the ground could be modeled b h = t + 5t. What is the initial velocit of the boiling water? b. What is the maimum height of the boiling water? c. How long is the boiling water in the air?. From 97 to 99, the average cost of a new car, C (in dollars), can be approimated b the model C = 3.5t + 9, where t is the number of ears since 97. During which ear was the average cost of a new car $,? 3. A punter kicked a -ard punt. The path of the football can be modeled b =.35 +.+, where is the distance (in ards) the football is kicked and is the height (in ards) the football is kicked. Find the maimum height of the football.. The average hourl earnings of U.S. production workers for 99-3 are shown in the table. Year 99 99 99 993 99 995 99 997 99 Avg. Hourl Earnings.9.5.7.3.3..3.9 3. Find the quadratic regression equation. b. Report the R value and discuss whether the quadratic model is appropriate. 5. Solve the quadratic equation a b c + + = b completing the square.