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24 Exploring the Quadratic Formula β Stations Objective: __________________________________________________________________________ Do Now: Answer the questions below: Station 1 1. At this station you will have 6 index cards. As a group flip over the 6 index cards and match each quadratic equation with the appropriate quadratic formula. Write the matches below. Station 2 1. At this station you will have a dice. Roll the dice once and write the number in the first box. Roll it again and write the number in the second box. 2. You can find the number and type of solutions to a quadratic equation by finding the discriminant. The discriminant is the value under the square root in the quadratic formula (π 2 β 4ππ). Find the discriminant of the quadratic equation you wrote in number 1. 2. Choose ONE of the quadratic equations and solve it below. 3. Based on your discriminant, what type of solution(s) does the quadratic function you created have? Explain how you know. 24 Station 3 1. At this station you find a word problem. The equation to model the word problem is: Solve the quadratic function using the quadratic formula. Station 4 1. At this station you will get a card with 4 scenarios, you need to determine whether there are two, one or no REAL solutions of each equation. Write down each scenario first! Scenario A: How many real solutions? Scenario B: 2. Which solution gives the amount of time it takes for the baseball to hit the ground? How many real solutions? Scenario C: How many real solutions? 3. Why will only one of your solutions equal the time it takes for the baseball to hit the ground? Scenario D: How many real solutions? Summary β use what you learned today in these stations to answer the questions that follow. 9π₯ 2 β 30π₯ + 25 = 0 1. Find the discriminant. 2. Based on the discriminant describe how many real solutions the quadratic equation has. Explain! 3. Solve using quadratic formula. 24 Station 1: Station 2: Dice Station 3: Station 4: The graph of the related quadratic function dos not have an x-intercept β none The graph of the related quadratic function touches but does not cross the x βaxis β one A quadratic equation has a discriminant equal to 0 β one Both a and b are greater than 0 and c is less than 0 in the quadratic equation - two