Quadratic formula and discriminant

Front

What is the quadratic formula?

Back

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

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 solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

If the discriminant is positive, how many real solutions does the quadratic equation have?

Back

Two real solutions.

Front

If the discriminant is zero, how many real solutions does the quadratic equation have?

Back

One real solution.

Front

If the discriminant is negative, how many real solutions does the quadratic equation have?

Back

No real solutions.

Front

What are the solutions of a quadratic equation also called?

Back

Roots, x-intercepts, or zeros.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, given by the coordinates (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a).

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 and a ≠ 0.

Front

What is the factored form of a quadratic equation?

Back

The factored form is expressed as a(x - r1)(x - r2) where r1 and r2 are the roots of the equation.