QuadFormula, Discriminant, Nonlinear Systems, Quad inequalities

Front

What is the formula for the discriminant in a quadratic equation?

Back

The discriminant is given by the formula: b² - 4ac.

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

If the discriminant is positive, there are two distinct real roots. If it is zero, there is one real root (a repeated root). If it is negative, there are no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is: ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you identify a, b, and c in the quadratic equation 4x² - 8x = 3?

Back

Rearranging to standard form gives 4x² - 8x - 3 = 0, so a = 4, b = -8, c = -3.

Front

What is a nonlinear system of equations?

Back

A nonlinear system includes at least one equation that is not linear, meaning it cannot be expressed in the form y = mx + b.

Front

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

Back

Graph both equations and count the number of intersection points. Each intersection represents a solution.

Front

What is the graphical representation of the solution set for the inequality x² - 5x - 14 > 0?

Back

The solution set is represented by the regions of the graph where the parabola is above the x-axis.

Front

How do you solve a quadratic inequality like x² - 5x - 14 > 0?

Back

First, find the roots of the corresponding equation x² - 5x - 14 = 0, then test intervals to determine where the inequality holds.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is given by: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert from standard form to vertex form?

Back

Use the method of completing the square to rewrite the quadratic equation in vertex form.