Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have two distinct real solutions, one real solution (a repeated root), or two complex solutions.

Front

What is the discriminant of a quadratic equation and how does it determine the nature of the roots?

Back

The discriminant is given by the formula D = b² - 4ac. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are two complex solutions.

Front

What is the Zero Product Property?

Back

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. This is used to solve equations in factored form.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, rewrite the equation in the form (x - p)(x - q) = 0, where p and q are the roots, and then set each factor equal to zero.

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 find the vertex of a quadratic function given in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is 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, given by the equation x = -b/(2a).

Front

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

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

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.