Solving Quadratic Equations (All Methods + Complex Solutions)

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.

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x). Then, rewrite the equation in factored form.

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Front

What are complex solutions in quadratic equations?

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Complex solutions occur when the discriminant is negative, resulting in solutions that include imaginary numbers, expressed in the form a + bi.

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How can you graph a quadratic equation?

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To graph a quadratic equation, plot the vertex, axis of symmetry, and intercepts, then draw a parabola opening upwards or downwards based on the sign of a.

Front

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, found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

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