Quadratic formula and discriminant

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What is the quadratic formula?

Back

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

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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.

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What does a positive discriminant indicate?

Back

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

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What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

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What does a zero discriminant indicate?

Back

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

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What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero; they are also called solutions or x-intercepts.

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How do you calculate the discriminant for the equation 6x² − 2x − 3 = 0?

Back

The discriminant is calculated as b² - 4ac = (-2)² - 4(6)(-3) = 4 + 72 = 76.

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What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upwards or downwards.

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What is the axis of symmetry in a quadratic function?

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

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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.