Algebra 1 EOC Review

Slope is the ______

Average Rate of Change

What do exponential DECAY graphs have?

Have a B of less than one

Exponential functions with a B more than 1

Are exponential growth graphs

What is the formula to find the point in the middle of a line segment

((x₁+x₂)/2) ((y₁+y₂)/2)

What are parallel lines

lines with the same slope

What are perpendicular lines

Lines with opposite reciprocal slopes (flipped and sign changed) Ex. 3/2--> -2/3

What is domain?

the x coordinates, input values, independent variables, on x axis

What is Range?

The y coordinates, output values, dependent variable, on the y axis

"adding or subtracting by the same amount" means…

The equation is an LINEAR function

"multiplying by the same amount" means…

The equation is an EXPONENTIAL function

When solving if all variables disappear this means it has

Infinitely Many Solutions

Line of best fit

a straight line that best represents the data on a scatter plot.

How to find the hypotenuse on a right triangle

Pythagorean Theorem

Exponent rule for power raised to a power

Multiply the exponents.

Power to a power rule

(x^a)^b = x^ab

Distance Formula

d = √((x2 - x1)² + (y2 - y1)²).

Exponent rule for dividing monomials

subtract the exponents.

Exponent rule for negative exponents

The reciprocal of the base is raised to the absolute value of the exponent, expressed as a fraction.

Product rule

x^a + x^b = x^a+b

Slope Intercept Form

y=mx+b

"Golden Rule" when solving Inequalities

If you multiply or divide both sides on inequality by a negative number, flip the inequality sign around.

Form of Exponential Equation

ab^x where a is a constant and b is the base raised to the power x.

Quadratic equation

ax² + bx + c = 0

How do you write the X intercept.?

(x, 0)

How do you write y-intercepts

(0. y)

the points where a graph crosses the x-axis, indicating the values of x for which the function is equal to zero.

x-intercept

"zeros of the function"

x-intercept

Factoring a quadratic (the first step is . . .)

Find the greatest common factor between the AX²+BX+C

Ways to Solve Systems of Equations

Substitution or Elimination or Graphing

Exponential Growth or Decay Formula for Word Problems

% increasing or decreasing

Function Notation

A way to represent functions using symbols such as f(x) to denote the output based on the input x, allowing for easier manipulation and understanding of relationships between variables.

What does f(x) mean?

y

Axis of Symmetry of a parabola

Vertical line through the vertex (x=-b/2a)

If "a" is positive

The parabola opens up

How do you tell if a parabola concaves down.

If "a" is negative

How do you find the vertex point of a parabola?

Use formula to find the AOS, then plug the AOS into the original equation to find the y.

(Strong vs. Weak and Pos. vs. Neg.)

Terms to describe correlations.

How do you tell if the slope of a line is negative or positive?

the direction of a line, indicating whether it rises or falls as it moves from left to right.

How do you know if the correlation is strong or weak?

The closer "r" is to 1 or -1, the stronger the fit.

Systems of Equations - Substitution Method

Put one equation into the other equations.

Systems of Equations - Elimination Method

Add or Subtract the 2 equations so that one of the variables "disappears"

When the problem says "Consecutive integers"…

Use X, X+1, X+2, X+3..

When the problem says "Consecutive Even or Odd integers" …

Use X, X+2, X+4, X+6

Find the slope from a table of values

change in Y divided by change in X

What is the visual representation of a line

The graphing of a line

b = starting point on y axis

m= rise/run

Slope

5 Number summery

minimum, Q1, Median, Q2, maximum

Q1

Middle number between Median and lowest number in data set

Q3

Middle number between median and largest number in Data set

IQR (Interquartile range)

Q3 - Q1

What is the slope-intercept form of a line?

y=mx+b

What kind of graph will y=mx+b create?

Linear Graph

slope

In the equation y=mx+b, what does "m" represent?

In the equation y=mx+b, what does "b" represent?

Y-intercept

What is the slope formula?

Y2-Y1/X2-X1

Slope is the ratio of ____ over ___

Rise, Run

What is the slope of a vertical line?

Undefined

0

What is the slope of a horizontal line?

Definition of a function

A relation where each x is paired with exactly one y

How do you use the vertical line test to tell if a graph is a function?

As the vertical line passes over the graph, the vertical line can only intersect the graph one time

What is the rule of dividing two powers with the same base?

Keep the base, subtract the exponents

exponents

What is the rule of multiplying two powers with the same base?

Keep the base, add the exponents

exponents

What is the standard form of a line?

Ax+By=C

When is it best to use your graphing calculator to solve a system?

When both equations are in slope-intercept form

When will a system have infinitely many solutions?

Same line (coinciding lines)

If you are given a point and a slope, explain how to find the equation.

Substitute the x, y, and m and solve for b. Write the equation using m and b.

Parallel lines

When will a system have no solution?

If given two points, how do you use your calculator to get the equation?

STAT, EDIT, Enter the x-coordinates into L1 and the y-coordinates into L2, Go to "STAT" again, then "CALC". Choose "4: LinReg(ax+b)", enter.

What should the answer to a system look like?

An ordered pair Ex: (x,y)

What are some ways to solve a system?

Graphing, Substitution, and Elimination

How do you find the x and y-intercepts of an equation?

Substitute 0 for y and solve for x.

Substitute 0 for x and solve for y

What is true about the slopes of parallel lines? Their y-intercepts?

Parallel lines have the same slopes, but different y-intercepts.

Perpendicular lines have slopes that are both opposite and reciprocal

What is true about the slopes of perpendicular lines?

What is the rule for taking a power to a power?

Keep the base, multiply the exponents

Move it to the opposite location (numerator/denominator) of the fraction bar and make the exponent positive

What is the rule for changing a negative exponent into a positive?

One

Any (nonzero) number to the zero power is equal to what?

What is the difference between an arithmetic and geometric sequence?

One adds the same number each time, and the other multiplies by the same number each time

How will you know if its growth or decay from looking at the equation?

In equation form: if b is greater than one, it is growth. If b is less than one and greater than zero, it is decay. In graph form: The graph of growth will increase.

from left to right ( a plane taking off). For decay, the graph decreases from left to right (a plane landing).

What is the standard form of an exponential equation?

y=ab^x

How many solutions should x²=16 have?

Two

What should be the first step when you factor?

Look for a GCF

What is the midpoint formula?

What is the distance formula?

What is a correlation coefficient and what does it tell you about the scatter plot/ line of best fit?

It is "r," and it tells you how closely your data fits the line of best fit. The r values range between -1 through +1.

What is the formula for the vertex form

y=a(x-h)²+k

What is the quadratic formula

-b ± square root of b² - 4AC all over 2A

Whats the arithmetic sequence formula

An=A1+d(n-1)

whats the geometric sequence formula

An=A1*r^n-1

Whats the point slope formula

y-y1=m(x-x1)

Whats the yearly compound interest formula.

A = P(1 + r)^t

What’s the interest rate formula.

I=PRT

What is the compound interest formula?

CI=P(1+r/n)^nt-P

What is the half life formula?

N(t)=N_o(1/2)^t/1/2t