Quadratic Formula

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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).

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

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation. If D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are no real solutions.

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If the discriminant is 25, how many solutions does the quadratic equation have?

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2 solutions.

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What does a positive discriminant indicate?

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A positive discriminant indicates that the quadratic equation has 2 distinct real solutions.

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What does a negative discriminant indicate?

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

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What does a zero discriminant indicate?

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A zero discriminant indicates that the quadratic equation has exactly 1 real solution (a repeated root).

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What is the standard form of a quadratic equation?

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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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Can all quadratic equations be factored?

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No, not all quadratic equations can be factored. The quadratic formula can be used to find solutions for those that cannot be factored.

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What is the vertex of a parabola?

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The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, depending on the direction it opens.

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How do you find the vertex of a quadratic function in standard form?

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The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.