# Chapter 2 2-6 Quadratic formula.

## Presentation on theme: "Chapter 2 2-6 Quadratic formula."β Presentation transcript:

Problem of the day If πβπ=β3 and π 2 β π 2 =24 then which of the following is the sum of n and m? A) -8 B)-6 C)-4 D)6 E)8

Answer to the problem of the day

Objectives Students will be able to : * Solve quadratic equations using the Quadratic Formula. * Classify roots using the discriminant.

Quadratic Formula You 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.

How does the quadratic formula works
By completing the square on the standard form of a quadratic equation, you can determine the Quadratic Formula.

The quadratic formula Often, 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.

Example #1 Find the zeros of f(x)= 2x2 β 16x + 27 using the Quadratic Formula.

Example #2 Find the zeros of f(x) = x2 + 3x β 7 using the Quadratic Formula.

Example #3 Use the quadratic formula to solve x2 + 3x β 4 = 0

Example #4 Find the zeros of f(x) = 4x2 + 3x + 2 using the Quadratic Formula.

Exampl#5 Find the zeros of g(x) = 3x2 β x + 8 using the Quadratic Formula.

Student guided Practice
Do problems 1-8 from the worksheet using quadratic formula

Discriminant 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.

Types ofdiscriminant

Example #6 Find the type and number of solutions for the equation.
x = 12x x2 β 12x + 36 = 0 b2 β 4ac find the discriminant (β12)2 β 4(1)(36) 144 β 144 = 0 Since b2 β 4ac = 0 The equation has one distinct real solution.

Example #7 Find the type and number of solutions for the equation.
x = 12x

Example#8 Find the type and number of solutions for the equation.
x2 β 4x = β4

Student guided practice
Find the type and number of solutions for each equation. A) x2 β 4x = β8 B) x2 β 4x = 2

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 = β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?