ALG 2 - COMPREHENSIVE REVIEW of Q2 (Pre-Thanksgiving) Concepts

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant indicates the nature of the roots of a quadratic equation. If it is positive, there are two distinct real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.

Front

How many solutions does a quadratic equation have if the discriminant is greater than zero?

Back

Two real solutions (which can be rational or irrational depending on the specific values).

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.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How do you determine the number of real solutions from the discriminant?

Back

If the discriminant (D) is positive, there are 2 real solutions; if D is zero, there is 1 real solution; if D is negative, there are no real solutions.

Front

What is the graphical representation of a quadratic equation?

Back

A quadratic equation is represented graphically as a parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic function in the form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting back to find y.