Quadratic Linear system

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

Front

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

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

Front

What does it mean for a quadratic function to have two real solutions?

Back

A quadratic function has two real solutions when its graph intersects the x-axis at two distinct points.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

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

Back

The number of solutions in a linear-quadratic system can be determined by analyzing the intersection points of the linear and quadratic graphs.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on the coordinate plane.