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 in a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct 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

Solve using the Quadratic Formula: 2x² + 2x - 12 = 0

Back

x = 2 or x = -3.

Front

True or False: The quadratic formula can be used to solve quadratic equations that cannot be factored.

Back

True.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8

Back

x = -8 or x = 4.

Front

What is the vertex of the quadratic equation y = x² + 4x - 6?

Back

The vertex is (-2, -10).

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a).

Front

How do you find the y-intercept of a quadratic equation?

Back

The y-intercept is found by evaluating the function at x = 0, which gives c in the equation ax² + bx + c.