Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What are 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 first step in solving a quadratic equation?

Back

The first step is to write the equation in standard form.

Front

True or False: The quadratic formula can be used to solve any quadratic equation.

Back

True.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

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

Front

In the equation x² + 4 = 0, what are the values of a, b, and c?

Back

a = 1, b = 0, c = 4.

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 of the parabola.

Front

How do you complete the square for the equation x² + 6x + 5 = 0?

Back

Rewrite as (x + 3)² - 4 = 0, then solve for x.

Front

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror images.