Solving Nonlinear Systems

Front

What is a nonlinear system?

Back

A nonlinear system is a system of equations in which at least one equation is not linear, meaning it cannot be represented as a straight line on a graph.

Tags

CCSS.HSA.REI.C.7

Front

How many solutions can a parabola have when intersecting a line?

Back

A parabola can have none, one, or two solutions when intersecting a line, depending on the position of the line relative to the parabola.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent lines or curves that do not intersect at any point.

Tags

CCSS.8.EE.C.8B

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation.

Front

How do you determine if a parabola opens upwards or downwards?

Back

If the coefficient of the x^2 term is positive, the parabola opens upwards; if it is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the number of real solutions: if positive, two solutions; if zero, one solution; if negative, no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

How can you graphically solve a system of equations?

Back

By plotting the equations on the same graph and identifying the points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is a maximum or minimum in the context of a parabola?

Back

A maximum is the highest point of a parabola that opens downwards, while a minimum is the lowest point of a parabola that opens upwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.