MR. STURDIVANT'S CLASS



Name Date ______________HSA.REI.B.4.BTeam Using the discriminant to determine the number of real solutionsKey Takeaways:Standard: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.Quadratic equations can have zero, one, or two real roots. You can determine the number of roots that a quadratic has by finding the discriminant (d=b2-4ac) and noticing:If d<0, there are no real rootsIf d=0, there is one real rootIf d>0, there are two real rootsVocabulary: Quadratic, root, solution, real solution, discriminant, x-intercept____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 1: Activation of Prior KnowledgeFor each quadratic equation below, determine the number of real roots it has. Write the number of solutions under each graph.A) y=2x2-x+4 B) y=x2+2x+1 C) y=x2+5x+43009902349500-38107620000762000Explain how you determined how many real roots each quadratic equation has.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 2: Guided PracticeThe ____________________________ is a part of the quadratic formula that can be used to determine the number of ____________________________ a quadratic equation has. Discriminant formula: _______________________Example 1: Calculate the discriminant for each of the equations from the APK. Use your calculations to fill out the table below.A) y=2x2-x+4 B) y=x2+2x+1 C) y=x2+5x+4300990901700025463554610002590805334000Value of discriminantNumber of real solutions the quadratic hasNegativeZeroPositiveExample 2: Determine the number of solutions to the equation below using the discriminant, then check the number of solutions by graphing on the coordinate plane.35585404254500y=x2 + 10x + 16=0Example 3: How many real solutions does the quadratic equation below have?y=x2 – 10x + 25One real solutionTwo real solutionsThree real solutionsNo real solutionsPart 3: Independent Practice (MILD)1) How many real solutions does the quadratic equation below have? 2x2-4x+5=0 123No real2) Find the discriminant of the equation x2-5x=0. 2521129Write the letter of the graph that matches the value of the discriminant below.9296408001000b2-4ac=2 _____________________b2-4ac=0 _____________________b2-4ac=-3 _______________________What is the discriminant of the function below?y=x2 – 10x + 3020-20-2200For which value of c will -3x2+6x+c=0 have only one real solution?c<-3c=-3c>-3c=3How many real solutions does x2-10x+25=0 have?No solutionsOne solutionTwo solutionsMany solutionsDetermine the number of solutions for each of the following quadratic equations. Use the discriminant to solve and then use your graphing calculator to check and make a sketch.x2-1=00123-51435254000x2-2x+1=00123-88905651500x2+3x+4=00123-12707747000Part 4: Independent Practice (MEDIUM)7) Determine the number of real roots for each equation in the table below. Then choose the statement below that is true about the number of real roots in each column.The total number of real roots in column A is greaterThe total number of real roots in Column B is greaterThe total number of real roots is equalThe relationship cannot be determined from the given information160020071120008) Determine the number of real solutions using the discriminant and then use your graphing calculator to check and sketch the graph.a) y = x2-4x-4 # of real solutions _____________________20955-190500b) y = -x2-3 # of real solutions ______________________20955-64262000c) y= -x2 - 1x +6 # of real solutions _____________________20955127000d) y = x2 -6x +9 # of real solutions _____________________20955-254000 9) How is the discriminant useful? Be specific. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 5: Independent Practice (SPICY)10. The length of a rectangle is 7 units more than its width. If the width is doubled and the length is increased by 2, the area is increased by 42 square units. Find the dimensions of the original rectangle.11. Which statement is true about the systems of equations below?2x+8y=6-5x-20y=-15It has no solutionIt has only one solutionIt has two solutions It has infinite solutions12. Ms. Blalock is selling tickets to a choral performance. On the first day of ticket sales the she sold 3 senior citizen tickets and 1 child ticket for a total of $38. She made $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. How much more does a child’s ticket cost than a senior citizen ticket? 445521448760I’m a mathleteI’m a mathlete4377447-194553“”“”5776365-197472MathletesName Date ______________HSA.REI.B.4.BTeam Using the discriminant to determine the number of real solutionsExit TicketDirections: Complete each problem by showing ALL work. Don’t forget to use MOLE! Determine the number of real solutions the equation below has by using the discriminant. Then, sketch the graph to confirm that your result is correct.420941524701500y=x2+8x+15What is the discriminant of the quadratic below?fx=x2-10x+25What does the discriminant that you calculated in #2 tell you about the number of real solutions that equation will have? Explain.________________________________________________________________________________________________________________________________________________________________________________________________________________________Name Date ______________HSA.REI.B.4.BTeam Using the discriminant to determine the number of real solutionsHomeworkDirections: Solve each problem. Show all work using MOLE. 1) Use the equation y = x2 – 6x + 5 to complete parts a-d.Factor and SolveUse the discriminant to find the # of solutions.Find the vertex. Graph the equation by using the solutions and the vertex and then label each one on your graph. 67437031750037795209842500380365100535002) 3)4) Which expression below is equivalent to 36b2-118b-118b+16b-16b+118b+118b+1(6b+1)(6b+1)5) How many roots does the graphed function shown have? 12750808509000OneTwoNoneThree 6) What is the rate of change for following table?66465817780000.20.5587) Which shows the following expression factored completely? 6x2 + 17x + 7(3x + 1)(2x + 7)(6x + 1)(1x + 7)(3x + 7)(2x + 1)(6x + 7)(1x + 1)8) What is the solution set to the following equation?k2-10k+26=8 ................
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