Using the Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What does it mean to 'complete the square'?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

How do you identify A, B, and C in a quadratic equation?

Back

In the standard form of a quadratic equation ax² + bx + c = 0, A is the coefficient of x², B is the coefficient of x, and C is the constant term.

Front

What is the discriminant in the context of the Quadratic Formula?

Back

The discriminant is the part of the Quadratic Formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

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

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What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

How can you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic equation in the form (x - p)(x - q) = 0, where p and q are the roots, and then set each factor to zero.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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 formula x = -b/(2a).