Solving Quadratics (All Methods)

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the leading coefficient in a quadratic equation?

Back

The leading coefficient is the coefficient of the term with the highest degree (x²) in a polynomial. In ax² + bx + c, it is 'a'.

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.

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means 2 real solutions, D = 0 means 1 real solution, and D < 0 means no real solutions.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros, set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

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 completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.

Front

What are the roots of a quadratic equation?

Back

The roots (or solutions) are the values of x that make the quadratic equation equal to zero.