Quadratic Formula and Discriminant

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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 (D) represent in a quadratic equation?

Back

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

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If the discriminant is zero, what can we conclude about the solutions of the quadratic equation?

Back

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

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What is the value of the discriminant for the equation 2x² + 4x + 2 = 0?

Back

The discriminant is D = 4² - 4(2)(2) = 16 - 16 = 0, indicating one real solution.

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How do you determine if a quadratic equation has two, one, or no real solutions?

Back

Calculate the discriminant (D = b² - 4ac). If D > 0, there are two solutions; if D = 0, there is one solution; if D < 0, there are no real solutions.

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What is the significance of a positive discriminant?

Back

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

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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, only complex solutions.

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For the quadratic equation x² - 4x + 4 = 0, what is the discriminant and how many solutions does it have?

Back

The discriminant is D = (-4)² - 4(1)(4) = 16 - 16 = 0, so it has one real solution.

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

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What does the vertex of a parabola represent?

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The vertex of a parabola is the highest or lowest point of the graph, depending on whether it opens upwards or downwards.