Quadratic Linear Systems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of 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 can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The number of solutions can be determined by analyzing the intersection points of the linear and quadratic graphs. Solutions exist where the graphs intersect.

Front

What does it mean if a linear-quadratic system has no solutions?

Back

It means that the graphs of the linear and quadratic equations do not intersect at any point.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the parabola changes direction, given by 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 nature of the roots.

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).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot both equations on the same coordinate plane and identify the points of intersection.