Quadratic formula and discriminant

Front

What is the quadratic formula used to find the solutions of a quadratic equation?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

What is the value of the discriminant for the equation x² + 4x + 4?

Back

The discriminant is zero, indicating that there is one real root.

Front

How do you determine if a quadratic equation has real solutions?

Back

Calculate the discriminant (b² - 4ac). If it is greater than or equal to zero, the equation has real solutions.

Front

What are the solutions of the equation 0 = x² + 5x + 7?

Back

There are no real solutions because the discriminant is negative.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean if the discriminant is positive?

Back

It means the quadratic equation has two distinct real solutions.

Front

What is the significance of the coefficients a, b, and c in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

Front

How can you solve a quadratic equation using factoring?

Back

Set the equation to zero, factor it into two binomials, and then set each factor equal to zero to find the solutions.

Front

What is the vertex form of a quadratic equation?

Back

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