Quadratic Linear Systems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, which means it can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a system of equations to have 0 solutions?

Back

A system of equations has 0 solutions when the lines or curves do not intersect at any point.

Front

What does it mean for a system of equations to have 1 solution?

Back

A system of equations has 1 solution when the lines or curves intersect at exactly one point.

Front

What does it mean for a system of equations to have 2 solutions?

Back

A system of equations has 2 solutions when the lines or curves intersect at two distinct points.

Front

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

Back

To find the intersection, set the linear equation equal to the quadratic equation and solve for x. Then substitute x back to find y.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, found at the coordinates (h, k) in the vertex form y = a(x-h)² + k.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the number of solutions.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).