Systems: Quadratic and Linear

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 to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is a linear equation?

Back

An equation that forms a straight line when graphed, typically in the form y = mx + b.

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants.

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 value of b² - 4ac, which determines the nature of the roots.

Front

What does it mean if the discriminant is positive?

Back

The quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

The quadratic equation has exactly one real root (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

The quadratic equation has no real roots, only complex roots.