Warm-up August 16, 2016 If the solutions to a quadratic equation are 2 and -3, what is the quadratic equation? Find the solution to the quadratic equation,

Unit 1: Quadratic Functions Review August 15, 2017 Unit 1: Quadratic Functions Review Daily Agenda Warm-up Imaginary Numbers – Review Solve Quadratic Equations using Square Roots Solve Quadratic Equations by Factoring Solve Quadratics using Quadratic Formula Direct Explanation Guided Practice – HW review Students will practice solving quadratic equations using various methods Independent practice #1 and #2 Worktime Address misconceptions Exit Slip – Error Analysis Closing

HW Review 8/15/2016

If a and b are real numbers and if , then or . 11.6 – Solving Quadratic Equations by Factoring Zero Factor Property: If a and b are real numbers and if , then or . Examples:

Solving Quadratic Equations: 1) Write the equation in standard form. 11.6 – Solving Quadratic Equations by Factoring Solving Quadratic Equations: 1) Write the equation in standard form. 2) Factor the equation completely. 3) Set each factor equal to 0. 4) Solve each equation. 5) Check the solutions (in original equation).

11.6 – Solving Quadratic Equations by Factoring

11.6 – Solving Quadratic Equations by Factoring If the Zero Factor Property is not used, then the solutions will be incorrect

11.6 – Solving Quadratic Equations by Factoring

11.6 – Solving Quadratic Equations by Factoring

11.6 – Solving Quadratic Equations by Factoring

11.6 – Solving Quadratic Equations by Factoring

11.6 – Solving Quadratic Equations by Factoring

Quadratic Equations Complete practice #1 – 19 odd Quadratic Equations Matching Game HW: complete practice #2 – 20 even

11.7 – Quadratic Equations and Problem Solving A cliff diver is 64 feet above the surface of the water. The formula for calculating the height (h) of the diver after t seconds is: How long does it take for the diver to hit the surface of the water? seconds

11.7 – Quadratic Equations and Problem Solving The square of a number minus twice the number is 63. Find the number. x is the number.

11.7 – Quadratic Equations and Problem Solving The length of a rectangular garden is 5 feet more than its width. The area of the garden is 176 square feet. What are the length and the width of the garden? The width is w. The length is w+5. feet feet

11.7 – Quadratic Equations and Problem Solving Find two consecutive odd numbers whose product is 23 more than their sum? Consecutive odd numbers:

11.7 – Quadratic Equations and Problem Solving The length of one leg of a right triangle is 7 meters less than the length of the other leg. The length of the hypotenuse is 13 meters. What are the lengths of the legs? meters meters

Solving Quadratic Equations by the Quadratic Formula

THE QUADRATIC FORMULA When you solve using completing the square on the general formula you get: This is the quadratic formula! Just identify a, b, and c then substitute into the formula.

WHY USE THE QUADRATIC FORMULA? The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it. An important piece of the quadratic formula is what’s under the radical: b2 – 4ac This piece is called the discriminant.

WHY IS THE DISCRIMINANT IMPORTANT? The discriminant tells you the number and types of answers (roots) you will get. The discriminant can be +, –, or 0 which actually tells you a lot! Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.

WHAT THE DISCRIMINANT TELLS YOU! Value of the Discriminant Nature of the Solutions Negative 2 imaginary solutions Zero 1 Real Solution Positive – perfect square 2 Reals- Rational Positive – non-perfect square 2 Reals- Irrational

Example #1 a=2, b=7, c=-11 Discriminant = Discriminant = Find the value of the discriminant and describe the nature of the roots (real,imaginary, rational, irrational) of each quadratic equation. Then solve the equation using the quadratic formula) 1. a=2, b=7, c=-11 Discriminant = Value of discriminant=137 Positive-NON perfect square Nature of the Roots – 2 Reals - Irrational Discriminant =

Example #1- continued Solve using the Quadratic Formula

Solving Quadratic Equations by the Quadratic Formula Try the following examples. Do your work on your paper and then check your answers.