Algebra I Exam Review Flashcards

These flashcards cover key concepts and problem-solving methods from Algebra I, based on the provided lecture notes.

What formula represents the height of a ball after bouncing off the ground?

h(t) = -16t^2 + 24t

In the expression 21,500(1 - rt), what does 21,500 represent?

The initial value of the car.

What does the term (1 - rt) represent in the car value equation?

It represents the percentage of the car's value remaining after depreciation.

What do you need to do to solve for x in the equation 2 + 4x = 6?

Isolate x by first subtracting 2 from both sides and then dividing by 4.

How do you find the maximum height of a bounce represented by the equation -16t^2 + 24t?

Find the vertex of the parabola by using the formula -b/2a to find t, then substitute t back into the equation.

What is the expression for the total amount spent on grapes and apples if grapes cost $2.50 per pound and apples cost $3 per pound?

The expression is y = 2.5g + 3a.

What does the total cost function y = 500 + 20x represent?

It represents the total cost including a flat fee and a charge per guest.

What is the evidence-based scale used for Algebra I standards?

The scale ranges from 1 (basic understanding) to 4 (beyond the standard).

What formula relates the height of a ball to the time after it is thrown?

h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.

What does it mean to isolate a quantity in a literal equation?

It means to rearrange the equation so that one variable is by itself on one side.

If you want to simplify (2t + 3) - (t - 4), what is the result?

The simplified expression is t + 7.

In polynomial expressions, how do you combine like terms?

Add or subtract coefficients of the same variable raised to the same power.

What is the result when you multiply (3x + 2)(2x - 1)?

The resulting polynomial is 6x^2 + 7x - 2.

Define a polynomial expression.

A polynomial expression is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

What is the process of factoring a quadratic function?

Finding two binomials whose product gives the original quadratic expression.

What is the slope-intercept form of a linear equation?

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

How do you solve a linear equation with two variables, like x + 2y = 10?

Use substitution or elimination methods to find the values of x and y.

What does the y-intercept represent in a linear function?

It represents the value of y when x equals zero.

How do you determine if a function is linear?

If the graph of the function is a straight line and can be expressed in the form y = mx + b.

What is the key feature of quadratic functions?

Quadratic functions have a parabolic graph, and they in the form y = ax^2 + bx + c.

What information does the vertex of a parabola provide?

The vertex indicates the maximum or minimum point of the quadratic function.

How can you represent a real-world problem with a linear equation?

By identifying the quantities and their relationships that can be expressed as linear functions.

What is the purpose of an inequality in mathematics?

An inequality shows the relationship between two expressions that are not equal but indicate the range of values for the variables.

How is compound interest calculated?

A = P(1 + r/n)^(nt), where P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.

What is the difference between simple and compound interest?

Simple interest is calculated on the principal only, while compound interest is calculated on the principal and also on any interest earned previously.

How do you find the domain of a function?

The domain consists of all possible input values (x-values) that will not cause any undefined operations.

What are the steps to graph a quadratic function?

1. Identify the vertex. 2. Determine the axis of symmetry. 3. Plot the y-intercept. 4. Calculate additional points on either side of the vertex.

Describe how to evaluate a function for a specific input. What does it involve?

Substitute the input value into the function's expression and simplify to find the output.

What transformation does the expression f(x + k) represent?

A horizontal shift of the graph to the left by k units.

How do you find the zeroes of a polynomial function?

Set the polynomial equal to zero and solve for the variable.

In a linear inequality, what does the symbol > or < indicate?

It indicates that the relationship between two expressions is strict, meaning one side is greater or less than the other.

What is a two-variable linear equation?

An equation that represents a relationship between two variables, typically written in the form Ax + By = C.

When combining functions algebraically, what does (f + g)(x) mean?

It means to add the outputs of f(x) and g(x) for any given value of x.

What is meant by the term 'residuals' when fitting a line to data?

Residuals are the differences between the observed values and the values predicted by the model.

What does the factor theorem state?

The factor theorem states that if you plug in a root of a polynomial function into the function and get zero, then the function has that root as a factor.

What is the significance of the discriminant in a quadratic equation?

The discriminant (b^2 - 4ac) indicates the nature of the roots (real and distinct, real and equal, or complex).

How do you evaluate radical expressions involving rational exponents?

Convert the radicals to rational exponents and then apply exponent rules for simplification.

What does it mean for a function to be continuous?

A continuous function can be graphed without lifting the pencil from the paper; there are no breaks or holes in the graph.

Provide an example of a quadratic function.

Example: f(x) = 2x^2 - 4x + 1.

How is the average rate of change calculated?

The average rate of change is calculated as the change in the function value divided by the change in the input value over a specified interval.

What can you conclude if the graphs of two functions intersect at several points?

The two functions have common outputs (y-values) at those particular x-values where they intersect.

How do you determine the maximum or minimum point in a quadratic function?

By finding the vertex of the parabola and determining its direction (upward or downward).