4.3 solving quadratic equations by factoring worksheet

#4.3 solving quadratic equations by factoring worksheet full#

We can use the Pythagorean Theorem to solve for x.Ĭheck on your own in the Pythagorean Theorem.Ģ000 450 − r + 2000 450 + r = 9 2000 450 − r + 2000 450 + r = 9 The distance from the base of the pole to either stake is the same as the height of the pole.Įach side is a right triangle. We are looking for the height of the pole. Since theĪnswers are approximate, the area will not come We eliminate the negative solution for the width. Then substitute in the values of a, b, c a, b, c.Īpproximate the answers using a calculator. Solve the equation using the Quadratic Formula. This is a quadratic equation rewrite it in standard form. Write the formula for the area of a rectangle. The height of the triangular window is 10 feet and the base is 24 feet.ģ w − 1 = 3 w − 1 = the length of the rectangle ĭoes a triangle with height 10 and base 24 have area 120? Yes. Since h is the height of a window, a value of h = −12 does not make sense. This is a quadratic equation, rewrite it in standard form. This will give us two pairs of consecutive odd integers for our solution.įirst odd integer n = 13 First odd integer n = −15 next odd integer n + 2 next odd integer n + 2 13 + 2 − 15 + 2 15 −13 First odd integer n = 13 First odd integer n = −15 next odd integer n + 2 next odd integer n + 2 13 + 2 − 15 + 2 15 −13ġ3, 15 yes − 13, −15 yes 13, 15 yes − 13, −15 yes There are two values of n that are solutions. The product of the first odd integer and the second odd integer is 195.

“The product of two consecutive odd integers is 195.” We are looking for two consecutive odd integers. One set of even integers and one set of odd integers are shown below. This is also true when we use odd integers. The next one would be n + 2 + 2 or n + 4. If we call the first one n, then the next one is n + 2. Remember, we noticed each even integer is 2 more than the number preceding it. We have solved number applications that involved consecutive even and odd integers, by modeling the situation with linear equations. Answer the question with a complete sentence Check the answer in the problem and make sure it makes sense. Solve the equation using algebra techniques. Then, translate the English sentence into an algebraic equation. It may be helpful to restate the problem in one sentence with all the important information. Choose a variable to represent that quantity. Make sure all the words and ideas are understood. Lessons can start at any section of the PPT examples judged against the ability of the students in your class. Main: Lessons consist of examples with notes and instructions, following on to increasingly difficult exercises with problem solving tasks.

Lesson 4.4.2h - Forming and solving quadratic equations (worded problems).

Lesson 4.4.1h - Forming and solving quadratic equations (geometric problems).

Lesson 4.3.2h - Completing the square - part 2 (a ≠ 1).

Lesson 4.3.1h - Completing the square - part 1 (a = 1).

Lesson 4.2.2h - The quadratic formula - part 2.

Lesson 4.2.1h - The quadratic formula - part 1.

Lesson 4.1.2h - Factorising harder quadratic equations (a ≠ 1).

Lesson 4.1.1h - Factorising quadratic equations (a = 1).

The worksheet could also be used independent of the PowerPoint lesson!

These are designed to speed up the lesson (no copying down questions etc). At least one printable worksheets for students with examples for each lesson.Normal PowerPoint lessons with which you can use a clicker / mouse / keyboard to continue animations and show fully animated and worked solutions.

#4.3 solving quadratic equations by factoring worksheet full#

A collection of EIGHT FULL LESSONS, which could definitely be extended to at least 10-11 lessons for the right classes, on solving quadratic equations by factorising, the quadratic formula or completing the square.