Quadratic/Discriminate Flashcard

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots of the quadratic equation ax² + bx + c = 0.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0.

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

What are the solutions of the quadratic equation x² - 4 = 0?

Back

The solutions are x = 2 and x = -2.

Front

How can you determine the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

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 equation x = -b/(2a).

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.