Algebra 2: Systems of Equations (Linear and Quadratic)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point.

Front

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

Back

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

Front

How can you determine the number of solutions in a linear-quadratic system?

Back

By finding the points of intersection between the linear equation and the quadratic equation.

Front

What is the general form of a quadratic equation?

Back

y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

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

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is b^2 - 4ac and determines the nature of the roots: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.