Math 1 Module 2 Solving Quadratics

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What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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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 can be found using factoring, completing the square, or the quadratic formula.

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What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How do you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 real roots; if D = 0, there is 1 real root; if D < 0, there are no real roots.

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What does it mean for a quadratic to be factored?

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Factoring a quadratic means expressing it as a product of two binomials, such as y = (x - r1)(x - r2), where r1 and r2 are the roots.

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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, depending on whether it opens upwards or downwards.

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How do you find the vertex of a quadratic function?

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The vertex can be found using the formula (-b/(2a), f(-b/(2a))) or by completing the square.

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What is the axis of symmetry in a quadratic function?

Back

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

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What is the significance of the leading coefficient in a quadratic function?

Back

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

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How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form ax² + bx + c = 0, factor it into (x - r1)(x - r2) = 0, and then set each factor to zero to find the roots.