Quadratic Formula

Front

What is the Quadratic Formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

Identify the values of a, b, and c in the equation: 4x² - 8x - 3 = 0.

Back

a = 4, b = -8, c = -3

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac.

Front

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

Back

It indicates that there are two distinct real roots.

Front

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

Back

It indicates that there are two complex (imaginary) roots.

Front

If the discriminant is zero, what can be said about the roots of the quadratic equation?

Back

There is exactly one real root (a repeated root).

Front

Solve for x: 3x² - 6x + 6 = 0.

Back

x = 1 ± i

Front

If the discriminant is positive but not a perfect square, how many solutions does the quadratic have?

Back

2 Irrational Solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

Front

What is the vertex form of a quadratic equation?

Back

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