Quadratic Equations with Real or Complex Solutions

Front

What is the quadratic formula?

Back

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

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They can be found by factoring the equation or using the quadratic formula.

Front

What shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is called a parabola.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, and it determines the nature of the roots.

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if it is negative, there are two complex roots.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How can you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting it back into the equation to find the y-coordinate.

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-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.