Quadratic formula

Front

What is the quadratic formula?

Back

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

Front

Identify the 'a' value in the quadratic equation y = ax² + bx + c.

Back

The 'a' value is the coefficient of x² in the equation.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the expression b² - 4ac, which determines the nature of the roots of the quadratic equation.

Front

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

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

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

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Front

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

Back

If the discriminant is negative, the quadratic equation has no real roots, but two complex roots.

Front

Determine the values of a, b, and c for the quadratic equation: 4x² – 8x - 3 = 0.

Back

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

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

You can convert by completing the square.

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 images.