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

Solve using the quadratic formula: 2x² + 7x - 15 = 0

Back

x = -5 or x = 3/2.

Front

What is the first step in solving x² + 6x - 13 = 3?

Back

Subtract 3 from both sides to set the equation to zero.

Front

Solve using the quadratic formula: 2x² + 2x - 12 = 0

Back

x = 2 or x = -3.

Front

Solve using the quadratic formula: 4x² + 4x + 1 = 0

Back

x = -½.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0.

Front

Can all quadratic equations be factored?

Back

No, some quadratic equations cannot be factored and must be solved using the quadratic formula.

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 the vertical line x = -b/(2a) that divides the parabola into two mirror-image halves.