Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring

Overview with Examples and Practice

There are several ways to solving a quadratic equation.

• 1) Graphing: Put the equation in Desmos and find the x-intercepts (zeros).

• 2) Factoring: Factor the trinomials, set each factor equal to zero, then solve for the indicated variable.

• 3) Quadratic Formula

• 4) Complete the Square

Solving a Quadratic Equation by Graphing

This is an objective that you should know how to do. Answer the question on the next slide to check your knowledge.

Multiple Select

Graph x² - x - 6 in Desmos. Find the zeros (x-intercept).

• 3

• 2

• -6

• -3

• -2

Prior Knowledge Needed

• Factoring Trinomials

• Solving Equations

• Checking your solution by graphing in desmos.

How to Solve a Quadratic Equations by Factoring:

• 1) Factor the trinomial.

• 2) Set each factor equal to zero.

• 3) Solve for the indicated variable.

• 4) Check your solutions.

Example #1

Solve x² - x - 6 = 0 by factoring.

Example #2

Solve x² + 6x + 9 = 0 by factoring.

Example #3

Solve 2x² - 9x + 10 = 0 by factoring.

Example #4

Solve 3x² + 5x + 2 = 0 by factoring.

I Understand. . .

that students will gravitate towards the easiest way to solve the quadratic equation: graphing. Therefore I will be testing to make sure that you are able to write the quadratic equation in intercept form (factored form) and solving equations.

So Let's Practice!

Take out a sheet of paper and answer the next four questions.

Open Ended

Solve for x.

(x + 3)(x - 3) = 0

Open Ended

Solve for x.

(4x - 3)(x +7) = 0

Open Ended

Write the intercept form for x² - x - 12 = 0.

Open Ended

Write the intercept form for 7x² - 6x - 1 = 0.

Poll

Which of the following concepts (steps) you still need help with?

• Factoring Trinomials (intercept form/factored form)

• Solving Equations

• I understand both concepts!!!