SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown.
1. What is the -ais measuring?. What is the y-ais measuring? 3. What are the units of the -ais? 4. What are the units of the y-ais? 5. At 10 seconds, what is the height? 6. How long did it take to get to 304 feet high? 7. What is the maimum point? 8. What is the maimum height? 9. How long does it take to get to the maimum height? 10. Why are there no points when the -coordinates are negative? 11. What is the y-intercept? 1. In a complete sentence, eplain what the y-intercept represents on this graph. 13. Where do you see the y-intercept in the equation? 14. How long does it take for the object to hit the ground? 15. What math vocabulary word(s) does this point represent? 16. Pick a point on the graph, eplain in complete sentences what that point represents on this graph.
SM Date: Objective: Section: Steps for solving stories: 1. READ the story, write down the information needed and define a variable. Write an equation 3. Solve for variable 4. Check Tips for solving story problems: Identify what you know. What are you trying to find out? Draw a picture or diagram to help you visualize the situation. Carefully define your variables. Translate the words into symbols. Use appropriate units. Make sure your answer makes sense. Hints: Sum: + Difference: Product: Quotient: Words that tell you to look for the verte: maimum, minimum, highest, lowest, biggest, littlest, largest, smallest, maimize, minimize. EXAMPLES: 1. A ski club sells calendars to raise money. The profit, P, in dollars, from selling calendars is given by the P = 10. equation ( ) Sketch a graph of the situation. Label the aes clearly. How much profit will the club make from selling 50 calendars? How many calendars must be sold for the club to make $700? How many calendars must be sold to maimize profit? What is the maimum profit?
. A rock is thrown upward from the ground by the wheel of a truck. Its height in feet above the ground after t ht = 16t + 0 t. seconds is given by the function ( ) Draw a sketch of the graph representing the path of the rock. What does each ais represent? How long does it take the rock to reach its maimum height? What is the maimum height of the rock? How long will it take for the rock to return to the ground? 3. A penny is thrown upward from the observation deck on the 10 nd floor of the Empire State Building. It s height, h, in feet, after t seconds is given by the equation ht ( ) = 16t + 9t+ 150 What is the height of the observation deck? (In other words, how high is the penny at t = 0? ) How high is the penny after seconds? The Empire State Building has a lightning rod with a tip that is 1454 ft above the ground. Will the penny reach the top of the lightning rod? (Hint: Find the maimum height and see if it s larger or smaller than 1454 ft.) When will the penny be 1110 feet above the ground? How long will it take for the penny to hit the ground?
SM Date: Section: Objective: Writing Quadratic Functions Given Key Features If you know the verte and another point on the parabola, or the roots and another point on the parabola, you can figure out the equation of the parabola. Writing a Quadratic Equation when You Know the Verte and Another Point 1. Use. Substitute in 3. Substitute in 4. (Don t forget ) 5. Write your final answer Eamples: Write an equation for each parabola described below. 1,, 0, 1 a) Verte: passes through b) Verte: 1, 3, passes through 3,5 c)
Writing a Quadratic Equation when You Know the Roots and Another Point 1. Use. Substitute in 3. Substitute in 4. (Don t forget ) 5. Write your final answer Eamples: Write an equation for each parabola described below. a) Roots: 1,0 and 3,0, passes through,9 b) Roots: 4,0 and 8,0, passes through 0,16 c)
Date: Section: SM Objective: f = + 3. Review Eample: Solve ( ) Notice that each of these inequalities below involves the value of + 3, which is represented by the y- coordinate of the graph. In each case, we are trying to figure out what -values (-coordinates) make the inequality true. When trying to find where + 3 > 0, we are trying to figure out what -coordinates have a y-coordinate that is bigger than zero in other words, where is the graph above the -ais? a) + 3> 0 b) + 3 0 ( ) f = + 3 c) + 3< 0 d) + 3 0
Solving a Quadratic Inequality Using the Graph: 1.... 3. If the inequality involves or, the -intercepts in the solution set ( or ). 4. If the inequality involves < or >, the -intercepts in the solution set ( or ). The solutions of The solutions of The solutions of The solutions of a + b + c > 0 are the -values for which the graph is the -ais. a + b + c 0 are the -values for which the graph is the -ais. a + b + c < 0 are the -values for which the graph is the -ais. a + b + c 0 are the -values for which the graph is the -ais. 5. Eamples: Solve each inequality and graph the solution set on a number line. Write answer in interval notation. a) ( 3)( + 1) 0 b) ( )( ) 7 5 < 0 c) + 5> 0 d) 4 1 0
e) 4< 0 f) + 10 9 g) 4+ 4> 0 h) 4+ 4 0 i) 4+ 4< 0 j) 4+ 4 0