FPMS Quadratic Formula

Front

What is the Quadratic Formula?

Back

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

Front

What does the discriminant tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

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

Back

For the equation 6x² − 2x − 3, the discriminant is calculated as D = (-2)² - 4(6)(-3) = 4 + 72 = 76.

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What is the significance of a negative discriminant?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, meaning the graph of the equation does not intersect the x-axis.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8.

Back

The solutions are x = -8 and x = 4.

Front

What are the roots of the equation 2x² + 2x - 12 = 0?

Back

The roots are x = 2 and x = -3.

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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.

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What does it mean if the discriminant is zero?

Back

If the discriminant is zero, it means the quadratic equation has exactly one real root, also known as a repeated or double root.

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How can you determine if a quadratic equation opens upwards or downwards?

Back

A quadratic equation opens upwards if the coefficient of x² (a) is positive, and it opens downwards if a is negative.

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What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola given by the equation y = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).