Word Problems modeled by Quadratic Equations

x + 1

x

1. Name what x is.

2. Define everything else in the problem in terms of x.

3. Write the equation.

4. Solve the equation.

5. Answer the question.

• Can only be one thing.• when in question choose smaller one.

• Start with concepts in ENGLISH.• Cross out as you go.

• Interpret what’s left using dictionary

Use the 5 Basic Steps to Solve Word Problems

Additional Factors...• The “area” of a shape is measured by the number of

squares that fit into it. • Quadratics involve squares… x2

• So area problems often end up as quadratic equations.• The area formula for a rectangle is... length • width

• The area formula for a triangle is... 1/2(length • width)

Don’t Forget...

• Quadratic Equations generally yield two answers.

• Length can never be negative.

• So only use the positive answers in an area problem.

1. Name what x is.2. Define everything else inthe problem.

The length of Joe’s kitchen floor is 4 feet more than the width. The area is 117 square feet. What is the length & width ?

x = the width the length = x + 4

3. Write the equation. x • (x + 4) = 117the area = x • (x + 4)

Area = Length • Width4. Solve the equation. x2 + 4x = 117

-117 -117 x2 + 4x - 117 = 0Solve by Factoring(x +13)(x - 9) = 0

x = -13 OR 95. Answer the question.The width is 9 (x)

The width can’t be negative

The length is 13. (x + 4)

1. Name what x is.

2. Define everything else inthe problem.

The sum of the squares of 2 consecutive negative integers is 221. What are the 2 numbers ?

x = the smaller integer

the next consecutive integer = x + 1

3. Write the equation. x2 =

square of the smaller integer = x2

square of the next consecutive integer = (x + 1)2

+ (x + 1)2 221

4. Solve the equation.

x2 = + (x + 1)2 2214. Solve the equation.

x2 = + (x + 1)(x + 1) 221

x2 + x2 + 2x + 1 = 221

2x2 + 2x + 1 = 221

-221 -221

2x2 + 2x - 220 = 0Solve by Factoring2(x2 + 1x - 110) = 0

2(x + 11)(x - 10) = 0

x = -11 OR 10

5. Answer the question.

The problem says the answer

MUST be negative

The smaller number is -11 (x) The next consecutive number is -10. (x + 1)

PRACTICE