Expressions & Equations

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Creating and solving Equations

By Morgan Pflum

Exponential equations are equations that utilize an exponent and the typical format of a(1 - r)^n, where a is the starting amount, r is the rate of growth or decay, and x is the amount of times it occurs. You will need to know how to create and solve exponential equations for the EOC.​

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​Exponential equations

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2^3x​ + 5 = 8

1. ​Rewrite so both sides have the same base. 2^3x + 5 = 2^3

2. ​Make the exponents equal and solve normally. 3x + 5 = 3

3. 3x = -2. x = -2/3.

​Solving exponential equations

​ 1. Write the format of a(1 - r)^n to begin writing.

2. Replace a with the starting amount, or principal.

3. Replace​ r with the percent decrease or increase (decay or growth).

4. Replace n with the amount of times the process takes place.​

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​Creating Exponential equations

Exponential equations: solving and making

Multiple Choice

Solve the following equation for x and y:

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2^x + 2^y = 20

x + y = 6

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• x = 2, y = 4

• x = 3, y = 3

• x = 3, y = 2

• x = 0, y = 2

Multiple Choice

Given that n and k are positive integers and $$8^{n\ }=\ 2^k$$  , then the value of $$\frac{n}{k}$$  is equal to what?

• 4

• 1/3

• 1/2

• 1/4

Multiple Choice

Who's this superb little guy?

• Zote the Mighty from the game Hollow Knight

• Cocomelon

• Electric Wizard :flushed: :flushed:

• your mother

Multiple Choice

James has a 70 inch giant peach. It doubles in size every week. Write an expression that would represent how big the peach is after x weeks.

• y = 2(70)^x

• y = 70(2)^x

• y = 1/2(70)^x

• y = 70(1/2)^x

Multiple Choice

Use the function N = 14,000(0.96)^x to represent the amount of money (N) owed for a loan. What doe 14,000 represent in this situation?

• The rate the loan is paid off.

• The amount of time passed.

• The starting amount of the loan.

• The percent decrease.

​Quadratic equations are also important to know for the EOC! You should know how to create/graph them. Quadratic equations are equations using the format ax^2 + bx + c = 0, in which a, b and c are constants.

What about quadratic equations?​​​

​Let's find out!!!!

​​How do i do it???

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QuadRatic graphs

Quadratic​ equations follow the format ax^2 + bx + c = 0, as mentioned. In the case of making them, you would replace a, b and c with the fitting constants. There's also vertex form-- (x - h)^2 + k --which is used to find... well, the vertex, and factored form-- (x - y)(x + z) --which tells us the x-intercepts.

To graph them, you use factored form to graph the x-intercepts​ and vertex form to find the vertex. Alternatively, you can use standard form to find out how to adjust the graph of x^2 (a parabola starting at the origin with no adjustments) to fulfill the equation.

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Multiple Choice

How many solutions does a quadratic equation have?

• They all have 0 solutions.

• They all have 0, 1, or 2 solutions.

• They all have 1 solution.

• They all have 2 solutions.

Multiple Choice

What shape is the graph of the function $$f\left(x\right)\ =\ 2x^2$$  ?

• Circle

• Hyperbola

• Parabola

• Ellipse

Multiple Choice

How about this little fella?

• Spelunky Guy

• Xero from a game with the initials H.K

• Rakim Stewart.

• Panther the cat

Multiple Choice

Is the vertex of the equation $$y=-6\left(x+4\right)^2+5$$  a minimum or a maximum?

• Minimum

• Maximum

• Neither

• Both

Multiple Choice

Which of these graphs are not a quadratic function?

​You guys get me.

Last but certainly not least:

Linear equations and how to solve and make them!​

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​Say you have an equation like -5x - 8 = 2(x + 10). First, you would use the distributive property to make it -5x - 8 = 2x + 20. then, add 5x to both sides to make -8 = 7x + 20. Subtract 20 from both sides to make -28 = 7x. Divide both sides by 7 to make -4 = x.

​Solving linear equations

Using the formatting of y = mx + b, in which​ m is the slope and b is the y-intercept, plug in the numbers needed. It's literally that easy.

​Making linear equations

Linear equations: solving and making

Multiple Choice

The cost of producing x tools by a company is given by C(x) = 1200x + 5500. What is the cost of 100 tools?

• 125,500

• 12,550

• 120,000

• 125,000

Multiple Choice

Find the equation for the line that goes through the two points (1,−2) and (−3,6)

• 5x - 4

• x/2

• y = -2x

• y = -4x

Multiple Choice

Who's this final fella?

• Troupe Master Grimm from Totally Not Hollow Knight

• littlest guy......

• Cocomelon Part 2: The Meloning

• Hog Rider Approaches

Multiple Choice

Solve for z. z - 5 = 6

• z = 6

• z = 10

• z = 5

• z = 11

Multiple Choice

Solve 3x - 5 = 10.

• x = 5

• x = 3

• x = 6

• x = 4

Open Ended

How do you graph linear, quadratic and exponential equations?

Poll

How did you like this lesson?

• I loved it!!

• It could have been better...

• Kind of boring.

• Worst quiz ever >:^(