Quadratic Formula

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 ax² + bx + c = 0.

Front

What does the discriminant (b² - 4ac) indicate?

Back

The discriminant indicates the nature of the roots of a quadratic equation: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

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

How can the Quadratic Formula be used?

Back

The Quadratic Formula can be used to solve quadratic equations that cannot be factored easily.

Front

Solve: 2x² + 7x - 15 = 0

Back

x = -5 or x = 3/2.

Front

Solve: x² + 9x + 20 = 0

Back

x = -4 or x = -5.

Front

Use the Quadratic Formula to solve: 2x² + 2x - 12 = 0

Back

x = 2 or x = -3.

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))).

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 images, given by x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the quadratic equation equal to zero.