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May 25th

May 25th

# Solving Linear and Quadratic Equations and Absolute Value Equations

Slide 23 Solving Quadratic Equations: Example

Hint: Before getting tangled up in arithmetic , think about what a
reasonable solution might be. Recall:

 Dose Weight Gain (dekagrams

If the animal gained 5 dekagrams, the dose was probably between 6
and 7.

Slide 24 Solving Quadratic Equations: Example

Hint: When possible, draw a picture .

Dose

Slide 25 Solving Quadratic Equations: Example

If the animal had gained 5 dekagrams, substituting for y ,

y = 5 = 1.13 − 0.41x + 0.17x2
5 −5 = 1.13 − 5 − 0.41x + 0.17x2
0 = 0.17x2 − 0.41x − 3.87

We can use the quadratic equation with

a
= 0.17, b = −0.41, c = −3.87
Slide 26 Solving Quadratic Equations: Example

We should go back and check these!

Slide 27 Solving Quadratic Equations: Example

The solutions to the equation are 6.127 and -3.715. Do both of
these make sense in the context of our problem? No - animals
cannot receive a negative dose ! We are only interested in solutions
greater than zero . The predicted dose is 6.127. (We can envision a
dose bigger than 6, but less than 7.) This agrees with our best
estimate before doing the math .
Slide 28 Absolute Value Equations

Recall: Absolute value refers to a number’s distance from 0 on
the real number line.

|a − b| is the absolute value of (a − b), or the distance from a to b
Example:

|5 − 3| = 2

Slide 29 Absolute Value Equations

a + b| can be thought of as |a − (−b)|, or the distance between a
and −b.

|5 + 3| = |5 − (−3)|, or the distance between 5 and -3, or 8.

| − a − b| = | − a − (+b)|, or the distance from −a to b

| − 5 − 3| = | − 5 − (+3)| = | − 8| = 8

Slide 30 Solving Absolute Value Equations

|a| = 5 means, “What values of a are 5 units away from 0?”
Solutions: 5 and -5

|a − 3| = 2 means, “What are the values of a such that the distance
between a and 3 is 2?”

We can deduce the answer by finding 3 on the number line and
finding the values 2 units away from 3.

Algebraically , we can solve the equations a −3 = 2 and a −3 = −2.
So a = 5 and a = 1

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