Quadratic Formula

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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).

Front

What does the discriminant tell us?

Back

The discriminant (D) is the part of the quadratic formula under the square root: D = b² - 4ac. It indicates the nature of the roots of the quadratic equation.

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What does a discriminant of 0 indicate?

Back

A discriminant of 0 indicates that the quadratic equation has exactly one real solution (a repeated root).

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What does a negative discriminant indicate?

Back

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

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What does a positive discriminant indicate?

Back

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

Front

Identify the coefficients in the equation y = x² + 5x + 7.

Back

a = 1, b = 5, c = 7.

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How do you calculate the discriminant?

Back

The discriminant is calculated using the formula D = b² - 4ac.

Front

Solve the quadratic equation x² + x - 56 = 0 using the Quadratic Formula.

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The solutions are x = 7 and x = -8.

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What is the leading coefficient in a quadratic equation?

Back

The leading coefficient is the coefficient of the x² term in the quadratic equation ax² + bx + c.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found using the formula (-b/(2a), f(-b/(2a))).