Q2 Benchmark Review

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting polynomial equation.

Front

What does it mean to find the zeros of a function?

Back

Finding the zeros of a function means determining the values of x for which the function equals zero.

Front

What is the significance of the zeros of a graph?

Back

The zeros of a graph indicate the x-intercepts, where the graph crosses the x-axis, and they represent the solutions to the equation.

Front

What is the process for checking solutions in rational equations?

Back

To check solutions, substitute the values back into the original equation to verify if both sides are equal.

Front

What is the difference between a rational expression and a rational equation?

Back

A rational expression is a fraction involving polynomials, while a rational equation is an equation that sets two rational expressions equal to each other.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify any restrictions on the variable that would make the denominator zero.

Front

What does the term 'extraneous solution' mean?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How can you identify the zeros of a quadratic function?

Back

The zeros of a quadratic function can be found using the quadratic formula, factoring, or by completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.