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).

Front

What does the discriminant tell us about a quadratic equation?

Back

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

Front

How do you identify a, b, and c in the quadratic equation 4x² - 8x = 3?

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Rearranging to standard form gives 4x² - 8x - 3 = 0. Here, a = 4, b = -8, c = -3.

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What is the first step in solving the equation x² + 6x - 13 = 3?

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The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

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Can the quadratic formula be used to solve equations that cannot be factored?

Back

Yes, the quadratic formula can be used to solve any quadratic equation, including those that cannot be factored.

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What is the vertex form of a quadratic equation?

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The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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What does it mean if a quadratic equation has no real solutions?

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It means that the graph of the quadratic does not intersect the x-axis, which occurs when the discriminant is less than zero.

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

Back

If the discriminant is positive, there are 2 solutions; if it is zero, there is 1 solution; if it is negative, there are no real solutions.

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

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The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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.