Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, 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 satisfy the equation, which 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 complete the square for the equation x² + bx?

Back

To complete the square, take half of b, square it, and add it to both sides of the equation.

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What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - a)² = x² - 2ax + a².

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How do you solve a quadratic equation by factoring?

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To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero and solve for x.

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What does it mean to solve by reversing?

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Solving by reversing involves isolating the variable by performing the inverse operations, such as taking the square root of both sides of an equation.

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What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

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How do you graph a quadratic function?

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To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a parabolic curve.

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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.