Quadratic Formula & Discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is 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 (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots.

Front

How can you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient of x² (a) is positive, and it opens downwards if a is negative.

Front

What are the zeros of a quadratic equation?

Back

The zeros of a quadratic equation are the values of x that make the equation equal to zero, also known as the roots of the equation.

Front

How do you find the zeros of a quadratic equation in factored form?

Back

To find the zeros of a quadratic equation in factored form (e.g., (x - p)(x - q) = 0), set each factor equal to zero: x - p = 0 and x - q = 0, then solve for x.

Front

What is the significance of the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the quadratic function.

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. It can be found using the formula x = -b/(2a).

Front

How do you use the quadratic formula to solve a quadratic equation?

Back

To use the quadratic formula, identify the coefficients a, b, and c from the equation ax² + bx + c = 0, then substitute them into the formula x = (-b ± √(b² - 4ac)) / (2a) to find the values of x.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, it means the quadratic equation has exactly one real solution, which is a repeated root.

Front

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

Back

The coefficients a, b, and c affect the shape, position, and orientation of the parabola represented by the quadratic equation y = ax² + bx + c.