Linear / Quadratic Systems of Equations

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 no solution?

Back

It means that the lines represented by the equations do not intersect; they are parallel.

Front

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

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means that the equations represent a line and a parabola that intersect at two distinct points.

Front

What is the standard form of a circle's equation?

Back

The standard form is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

The center can be found from the equation (x - h)² + (y - k)² = r² as (h, k).

Front

What is the radius of a circle given the equation (x + 2)² + (y - 3)² = 16?

Back

The radius is 4, since r² = 16, so r = √16 = 4.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, 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.