Solving Quadratics using Casio Calculator

Step 1: Use inverse operations to get your quadratic in ax² + bx + c = 0

Step 2: Identify a, b and c (the coefficient for x², coefficient for x and the constant.

Step 3: Navigate to the EQUA app → choose “F2: Polynomial”→DEGREE OF 2 (quadratic)

 

Step 4: Enter in a, b and c and press solve.

 

Step 5: You’ve got your solutions!

 

J.4 Solve a Quadratic Equations Using Square Roots

Use this method when your polynomial does not have a b term.

1. Isolate the x² term (if not already done)
2. Take the square root of each side to get x by itself.
   1. When you √x² you are left with x.
   2. When you √ the opposite side, you get 2 answers
      1. The answer itself
      2. – answer

Special Notes:

Your Calculator will completely simplify any √  so USE IT.

The reason we must give the + and – of each answer is because (-x)² = x²

Example:

1. Isolate the x² term  – Already done

2. Square root each side.

3. √ x² = x

 

4. √ opposite side IN CALCULATOR!!

5. x = + answer and x = -answer

 

J.8 – Completing the Square

 

1. Divide b (coefficient of x term) by 2.
2. Square the result.
3. Add it to the end of the polynomial

Special Notes:

• This pattern is works for ANY polynomial where a = 1.

 

Example;

1. Divide b (-6 in this problem) by 2.

 

 

2. Square the result and add it to the end of the polynomial.

 

 

Factoring Quadratic Trinomials (ALL TYPES)

Bellow you will find steps and examples for factoring any type of quadratic trinomial.  The are listed in increasing order of difficulty, just like IXL.

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ax² + bx + c

Level 1: a = 1

Step 1: Find the factors of c (numbers that multiply to equal c)  that add up to b.

Step 2: Create binomials with these factors in the form:                                                   (variable ± first factor)(variable ± second factor)

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ax² + bx + c

Level 2: a = GCF

Steps:

1. Find a greatest common factor for your a , b  and c terms.

2. Divide out the GCF from a , b  and c.

 

3. Write out (or mentally think of) the factors of your NEW c term.

 

4. Choose the factors of c that add up to the NEW coefficient b

 

5. Write these factors as binomials (x ± first factor)(x ± second factor)

6. Bring down the initial GCF you factored out, and multiply it by your newly created binomials.  You’re done!

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Level 3: a ≠ 1, but a, b and c have no GCF

Step 1: Draw your factor X and fill in top (with a*c) and bottom (with b).

Step 2: Find the FACTORS of the TOP term (numbers that multiply to equal the top term) that add up to your BOTTOM term.  Put these factors on the sides of your X.

Step 3: Take the coefficient, a and multiply it by the variable in your problem. Put this term over the numbers on the sides of your X.

Step 4: Simplify the fractions (if possible).

Step 5: Write factors in binomial form:                                                                                   (numerator +/- denominator) (numerator +/- denominator)

 

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ax² + bx + c

Level 4: a ≠ 1 and a, b and c have a GCF

Step 1: Factor out GCF from a, b and c (if possible)

 

Step 2: Draw your factor X and fill in top (with a*c) and bottom (with b).

Step 3: Find the FACTORS of the TOP term (numbers that multiply to equal the top term) that add up to your BOTTOM term.  Put these factors on the sides of your X.

Step 4: Take the coefficient, a and multiply it by the variable in your problem. Put this term over the numbers on the sides of your X.

Step 5: Simplify the fractions (if possible).

Step 6:  Write factors in binomial form:                                                                                   (numerator +/- denominator) (numerator +/- denominator)

Step 7: Bring down the GCF (if you factored one out in step 1) and you’re done!

Factoring Trinomials (When a is NOT 1 or GCF)

ax² +bx + c

Step 1: Factor out GCF from a, b and c (if possible)

 

Step 2: Draw your factor X and fill in top (with a*c) and bottom (with b).

Step 3: Find the FACTORS (numbers that multiply to) of the TOP term that add up to your BOTTOM term.  Put these factors on the sides of your X.

Step 4: Take the coefficient, a and multiply it by the variable in your problem. Put this term over the numbers on the sides of your X.

Step 5: Simplify the fractions (if possible).

Step 6:  Write factors in binomial form:                                                                                   (numerator +/- denominator) (numerator +/- denominator)

Step 7: Bring down the GCF (if you factored one out in step 1) and you’re done!

Factoring Trinomials (When a is GCF)

**When we refer to trinomials, we use the notation:

ax² + bx + c

Where a, b are the coefficients of x² and x and c is the constant.

Steps:

1. Find a greatest common factor for your a , b  and c terms.

2. Divide out the GCF from a , b  and c.

 

3. Write out (or mentally think of) the factors of your NEW c term.

 

4. Choose the factors of c that add up to the NEW coefficient b

 

5. Write these factors as binomials (x ± first factor)(x ± second factor)

6. Bring down the initial GCF you factored out, and multiply it by your newly created binomials.  You’re done!

Factoring by Grouping

Step 1: Decide if ALL of the terms have anything in common. If so, factor out this number called the GCF (Greatest Common Factor). Do not forget to include this GCF as part of your final answer.

Step 2: Find pairs of terms with common factors within the problem.  This is usually done by grouping the first two terms together and the last two terms together (in a 4 term polynomial).

Step 3: Pull out the common factors in the FIRST pair of terms.

Step 4: Pull out the common factors in the SECOND pair of terms.  Make sure that your “leftover binomial” matches with the first “leftover binomial”

Step 5: Take each of your “Factored out” terms and create a new binomial.

Step 6: Write the matching leftover binomial next to it as a multiplication problem and DON’T FORGET ANY GCF YOU INITIALLY FACTORED OUT!

 

Step 7: You’re done!