Quadratic Formula and Discriminant ***

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant in a quadratic equation represent?

Back

The discriminant, represented as D = b² - 4ac, determines the nature of the roots of the quadratic equation.

Front

If the discriminant is positive, what can be said about the solutions of the quadratic equation?

Back

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

Front

If the discriminant is zero, what can be said about the solutions of the quadratic equation?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

Front

If the discriminant is negative, what can be said about the solutions of the quadratic equation?

Back

If the discriminant is negative, the quadratic equation has no real solutions (the solutions are complex).

Front

How do you identify the 'b' value in a quadratic equation?

Back

In the quadratic equation of the form y = ax² + bx + c, the 'b' value is the coefficient of the x term.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

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.

Front

How can you determine the number of solutions using the discriminant?

Back

By calculating the discriminant (D = b² - 4ac), you can determine the number of solutions: D > 0 (two solutions), D = 0 (one solution), D < 0 (no solutions).

Front

What is the vertex of a parabola in relation to a quadratic equation?

Back

The vertex of a parabola is the highest or lowest point of the graph of the quadratic equation, found at the point (h, k) where h = -b/(2a) and k is the value of the quadratic at h.