2Problem of the dayIf 𝑛−𝑚=−3 and 𝑛 2 − 𝑚 2 =24 then which of the following is the sum of n and m?A) -8B)-6C)-4D)6E)8
3Answer to the problem of the day Solution is Answer A
4ObjectivesStudents will be able to : * Solve quadratic equations using the Quadratic Formula.* Classify roots using the discriminant.
5Quadratic FormulaYou have learned several methods for solving quadratic equations: graphing, making tables, factoring, using square roots, and completing the square. Another method is to use the Quadratic Formula, which allows you to solve a quadratic equation in standard form.
6How does the quadratic formula works By completing the square on the standard form of a quadratic equation, you can determine the Quadratic Formula.
7The quadratic formulaOften, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution.
8Example #1Find the zeros of f(x)= 2x2 – 16x + 27 using the Quadratic Formula.
9Example #2Find the zeros of f(x) = x2 + 3x – 7 using the Quadratic Formula.
10Example #3Use the quadratic formula to solve x2 + 3x – 4 = 0
11Example #4Find the zeros of f(x) = 4x2 + 3x + 2 using the Quadratic Formula.
12Exampl#5Find the zeros of g(x) = 3x2 – x + 8 using the Quadratic Formula.
13Student guided Practice Do problems 1-8 from the worksheet using quadratic formula
14Discriminant What is the discriminant? The discriminant is part of the Quadratic Formula that you can use to determine the number of real roots of a quadratic equation.
16Example #6 Find the type and number of solutions for the equation. x = 12xx2 – 12x + 36 = 0b2 – 4ac find the discriminant(–12)2 – 4(1)(36)144 – 144 = 0Since b2 – 4ac = 0The equation has one distinct real solution.
17Example #7 Find the type and number of solutions for the equation. x = 12x
18Example#8 Find the type and number of solutions for the equation. x2 – 4x = –4
19Student guided practice Find the type and number of solutions for each equation.A) x2 – 4x = –8B) x2 – 4x = 2
20Quadratic formula applications An athlete on a track team throws a shot put. The height y of the shot put in feet t seconds after it is thrown is modeled by y = –16t t The horizontal distance x in between the athlete and the shot put is modeled by x = 29.3t. To the nearest foot, how far does the shot put land from the athlete?
21Quadratic formula applications A pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of the water t seconds after its release is modeled by y = – 16t2 – 2t the horizontal distance x in feet between the water and its point of release is modeled by x = 91t.The pilot’s altitude decreases, which changes the function describing the water’s height to y = –16t2 –2t To the nearest foot, at what horizontal distance from the target should the pilot begin releasing the water?