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 ax + b = 0, where a and b are constants.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Front

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

Back

To find the intersection graphically, plot both equations on the same set of axes and identify the points where the two graphs intersect.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola, and it represents the maximum or minimum value of the function.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

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, and it determines the nature of the roots of the equation.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots, but two complex roots.