Check In 2 Review

Check In 2 Practice

By Elzy Jay Lindsey

​Graph of a quadratic

When you graph a quadratic. Say, for instance, a person is throwing a rock off a cliff into the ocean, and they want to know when the rock hits the water. It is the greater zero of the function. You must factor the quadratic and find the greater zero.

Domain of a function

The domain of a function are its x-values. Think of any values that COULD NOT be true for x. Could x be negative?

​Exponential Growth

When determining exponential growth, you have to divide your percent by 100. So, if something is 1.2.% growth 1.2/100 = 0.012, then you add that decimal to 1, so the growth factor is 1.012

Non-routine problems

If you’re trying to find the SUM of x & y you add them, the difference is subtraction, the product is multiplication.

The sum of 2 numbers, x & y is 12, their difference is 2. What is their product?

​Solving systems by elimination

Solving systems by elimination means adding the 2 equations together to remove the opposite coefficients. Then solve for the other variable.

​Average with missing value

 When you find the average and you’re missing a value use x for the missing value. Set up an equation were you’re adding the numbers and x = to the average. Divide both slides by the number of numbers (and x). Multiply the denominator away from both sides then add the numbers on the left. Finally subtract them from the average number(which you multiplied times the denominator)

​Distance between zeros

The distance between the zeros of a function means how far apart on the x-axis are they? So factor the trinomial then see how far the 2 x’s are apart.

​Systems by substitution

When you solve an equation by substitution but one equation still needs to be put in y=mx+b form. Put the equation that is closest to y=mx=b in that form then take the mx+b part and put that into the other equation in place of y. Solve for x.

​Linear equations

Leo has a job selling t-shirts at the circus, he earns $15 per game plus $0.50 for each shirt he sells. How many shirts does he need to sell to make $25?

Equation from a table

Equation from a table the slope is how the y-values are changing. The y-intercept is what y is when x = 0.

​Break-even point

The break even point is when the lines intersect (the solution to the system).

​Polynomial arithmetic

Multiply the first trinomial times 3, then the second one times 5, then subtract the second from the first to solve 3f(x)-5g(x)
f(x)= 2x²+3x-5 g(x)= 6x²+7x-1

Difference in maximum values

Difference in maximum values in quadratics. Graph both in Desmos, maximum are the vertex in each. Count the spaces between the 2, if diagonal use distance formula.

​Difference between y-intercepts

 Difference between 2 y-intercepts. First equation is line through 2 points do a linear regression (y1~mx1+b), graph the second and count the space between the 2 y-intercepts.

The graph of a linear function passes through the points (2, 7) & (4, 12)
A second linear function is y=-2x +6. What is the difference between their y-intercepts?

​Exponential decay

Percent decrease is subtracted from 1, so if the equation is
y =30(0.75)^x the percent decrease is -0.25 or 25% off.
The original price is $30 (the y-intercept). And the sale price is 75% of what it USED TO BE or 25% OFF (1 - 0.25 = 0.75).

​Range of a function

Domain are the x-values that is 3 -10, plug those into the equation to get the OUTPUTS that is the range.

​Exponential functions

y=a(b)^{x
a=initial amount
b=growth factor
x=number of times (years)}

​Changing dimensions

If I double the length and width what happens to the area?

​Domain of a function

What are the possible x-values of this function?

​Equations vs. tables

Drop both into Desmos. If you need to find any info from a table, do y₁~mx₁+b and get all the regression data (m= slope, b= y-int, r = correlation coefficient, e₁ plots residuals). If you need to compare slopes or intercepts just use this info.
*** Remember, you can plot points by putting them into a table and doing a regression to make a line and get all this valuable info.

​Polynomial word problem

Area of shaded region outside of another rectangle (binomial side lengths)
Inside (w=x, l = 2x)
Outside (w=x+2, l =2x+3)

​Linear model

A family purchased a television 4 years ago. 3 years ago it was worth $430. Last year it was worth $340. How much did they originally pay?

If you want to figure this out, make a table with the points (1, 430) and (2, 340). The numbers one ans 2 stand for the number of years they have owned the TV. so, when they owned the TV one year it was worth 430, and when they owned it for 2 years it was worth 340.
Do a linear regression between the 2 points to get the y-intercept (the initial price of the TV).

​Systems by graphing

Plug into Desmos.
Remember to check for the exact answer they are asking for...
are they asking for the solution?
the x-value?
the y-value?

​Domain

Domain are the x-values of a function. Which values could be TRUE for x?

​Growth/decay factors

Remember that these are the b values in y=a(b)^x.
You must take the percent and divide by 100 to get the decimal amount of growth or decay, than ADD or SUBTRACT this value from 1.