Unit 1.3 Working with Formulas

Define perimeter

The distance around a shape

Define area

The surface covered by a shape

Define volume

Space occupied

What is the formula for volume?

Volume = length X width X height

What would be the units when calculating volume? Use meters as an example

m³

What is the formula for the area of a triangle?

Base X Height / 2

What are the units when describing area? Use cm for an example

cm²

What are the two algebraic methods of working with formulas?

• Substituting all known values first, then solving for the unknown

• Isolating the unknown first, then substituting all known values

What are the three main types of functions?

• Linear

• Quadratic

• Exponential

Linear functions are typically written in what form?

y = mx + b

In y = mx + b, what do the m and b represent?

• m is the slope

• b is the y-intercept

Are linear equations graphed as a straight line?

Yes

In quadratic equations, what is the highest exponent it can have?

x²

What is the typical form of quadratic equations?

y = ax² + bx + c

In quadratic equations, what number can a never be?

a can never equal 0

When graphed, what does a quadratic equation look like?

A parabola

In exponential equations, what is the variable x?

An exponent

What is the typical formula for exponential equations?

y = ab^x

What does an exponential equation look like when graphed?

A smooth curve that opens either up or down

If an exponent is a variable and you can’t nicely make the equation have equal bases, what can you do?

Graph it and use the x in a pair (i.e. (x, y))

How do you get from a decimal to a percentage? e.g. 0.065

• Multiply by 100

• 0.065 X 100 = 6.5%

If we want to get rid of an exponent of ², what do we do? e.g. 1.135 = (1 + x)²

Take the square root of both sides to eliminate the exponent

What is a way to verbally say this?

“4th root of 20”

If we want to eliminate an exponent, what can we do? e.g. x⁴

• Multiply by the reverse fraction and it will cancel it out (remember to do the other side of the equation as well)

• (x⁴) ^1/4