Math Focus: Intro to Quadratic Equations

Intro to Quadratic Equations

(LM 27_Math Focus 1-2)

Lesson GOALS:

• Identify quadratic equation.

• Write quadratic equations in standard form.

• Identify a, b and c.

Identifying the terms of a quadratic equation

Observe how the values of a, b and c are identified in the given quadratic equation in this illustration.

Open Ended

Why should $$a\ne0$$  in a quadratic equation of the form  $$ax^2+bx+c=0$$ ?

Elaborate on what happens to the equation when a = 0. 

Multiple Select

Activity 2 (1-5): Quadratic Or Not

Identify which of the following equations are quadratic and which are not.

(Choose all equations that are quadratic equations.)

• $$3m+8=15$$  

• $$x^2-5x+10=0$$  

• $$12-4x=0$$  

• $$2t^2-7t=12$$  

• $$6-2x+3x^2=0$$  

Quadratic Equations for Nos. 1-5

Multiple Select

Activity 2 (6-10): Quadratic Or Not

Identify which of the following equations are quadratic and which are not.

(Choose all equations that are quadratic equations.)

• $$25-r^2=4r$$  

• $$3x\left(x-2\right)=-7$$  

• $$\frac{1}{2}\left(h-6\right)=0$$  

• $$\left(x+2\right)^2=0$$  

• $$\left(w-8\right)\left(w+5\right)=14$$  

Quadratic Equations for Nos. 6-10

Multiple Choice

Activity 3: Set Me to Your Standard

Identify the equivalent quadratic equation in standard form of the given. Also, correctly identify the values for a, b and c.

1.  $$3x-2x^2=7$$  

• $$-2x^2+3x+7=0;$$  

  $$a=-2,\ b=3,\ c=7$$  

• $$-2x^2+3x-7=0;\$$  

  $$a=-2,\ b=3,\ c=-7$$  

Multiple Choice

Activity 3: Set Me to Your Standard

Identify the equivalent quadratic equation in standard form of the given. Also, correctly identify the values for a, b and c.

2.  $$5-2x^2=6x$$  

• $$-2x^2-6x+5=0;$$  

  $$a=-2,\ b=-6,\ c=5$$  

• $$-2x^2+6x+5=0;\$$  

  $$a=-2,\ b=6,\ c=5$$  

Multiple Choice

Activity 3: Set Me to Your Standard Identify the equivalent quadratic equation in standard form of the given. Also, correctly identify the values for a, b and c. 3.  $$\left(x+3\right)\left(x+4\right)=0$$  

• $$x^2+7x+12=0;\$$  

  $$a=1,\ b=7,\ c=12$$  

• $$x^2+x+12=0;\$$  

  $$a=1,\ b=1,\ c=12$$  

Multiple Choice

Activity 3: Set Me to Your Standard

Identify the equivalent quadratic equation in standard form of the given. Also, correctly identify the values for a, b and c.

4.  $$\left(2x+7\right)\left(x-1\right)=0$$  

• $$2x^2+6x-7=0$$  

  $$\ a=2,\ b=6,\ c=-7$$  

• $$2x^2+5x-7=0;$$  

  $$\ a=2,\ b=5,\ c=-7$$  

Multiple Choice

Activity 3: Set Me to Your Standard

Identify the equivalent quadratic equation in standard form of the given. Also, correctly identify the values for a, b and c.

5.  $$2x\left(x-3\right)=15$$  

• $$2x^2-6x+15=0$$  

  $$\ a=2,\ b=-6,\ c=-15$$  

• $$2x^2-6x-15=0;$$  

  $$\ a=2,\ b=-6,\ c=-15$$  

Congratulations!

You have accomplished this introductory lesson on Quadratic Equations!

Continue reading Module 27 on how to Solve Quadratic Equations.

Don't forget to click TURN IN, as you have accomplished this lesson.