Linear/Quadratic Systems of Equations (YL Flashcard)

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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 and a ≠ 0.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

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

Front

What does it mean for a system of equations to have two solutions?

Back

It means the equations intersect at two distinct points, which can occur in certain quadratic-linear systems.

Front

How do you find the intersection of a linear and a quadratic equation?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the graphical representation of a quadratic equation?

Back

A parabola, which can open upwards or downwards depending on the coefficient of x².

Front

What is the vertex of a parabola?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The value calculated as b² - 4ac, which determines the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.