Solving non-linear systems

Front

What is a non-linear system?

Back

A non-linear system is a set of equations where at least one equation is not linear, meaning it cannot be represented as a straight line on a graph.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the intersection points of two equations?

Back

To find the intersection points, solve the equations simultaneously, either by substitution or elimination, or by graphing.

Front

What does it mean to graph a quadratic function?

Back

Graphing a quadratic function involves plotting points that satisfy the equation and connecting them to form a parabola.

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

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine if a point is a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system when substituted into them.

Front

What is substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.