Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots of the quadratic equation. If it is positive, there are two distinct real solutions; if zero, there is one real solution; if negative, there are two complex solutions.

Front

How do you simplify √-4?

Back

√-4 can be simplified to 2i, where i is the imaginary unit.

Front

What are the values of a, b, and c in the equation 4x² – 8x = 3?

Back

In the equation 4x² – 8x - 3 = 0, the values are a = 4, b = -8, and c = -3.

Front

What is the significance of a zero discriminant in a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution, meaning the parabola touches the x-axis at one point.

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 of the parabola.

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form ax² + bx + c is given by the formula x = -b/(2a).

Front

What is the relationship between the coefficients of a quadratic equation and its graph?

Back

The coefficients a, b, and c determine the shape, direction, and position of the parabola on the graph.

Front

What does it mean for a quadratic equation to have complex solutions?

Back

Complex solutions occur when the discriminant is negative, resulting in solutions that include imaginary numbers.

Front

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

Back

To convert from standard form to vertex form, you can complete the square.