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

What are the coefficients a, b, and c in a quadratic equation?

Back

In a quadratic equation of the form ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

Identify a, b, and c for the quadratic equation: 3x² + 2x - 5 = 0.

Back

a = 3, b = 2, c = -5.

Front

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

Back

The discriminant indicates the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

Front

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

Back

x = 2 (double root).

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 and can be found using the formula (-b/(2a), f(-b/(2a))).

Front

How do you determine if a quadratic equation opens upwards or downwards?

Back

If the coefficient 'a' in ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

Solve using the quadratic formula: 2x² + 3x - 5 = 0.

Back

x = 1 and x = -5/2.

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.