Algebra 2 Final Exam Extra Practice

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as a coordinate (h, k) in the vertex form of a quadratic equation y = a(x-h)² + k.

Front

What are the solutions to a quadratic equation?

Back

The solutions, also known as roots or zeroes, are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

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 does it mean if a quadratic function has no real solutions?

Back

It means the graph of the function does not intersect the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.

Front

What are x-intercepts?

Back

X-intercepts are the points where a graph crosses the x-axis, corresponding to the solutions of the equation when y = 0.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set the quadratic equation equal to zero and solve for x using factoring, the quadratic formula, or graphing.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is a linear system?

Back

A linear system consists of two or more linear equations that can be solved simultaneously to find the values of the variables.

Front

What does it mean for a linear system to have no solutions?

Back

It means the lines represented by the equations are parallel and never intersect, indicating that there is no set of values that satisfies all equations.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.