Solving Quadratics and Quadratic Formula

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 quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, there are two distinct real roots; if = 0, there is one real root (a repeated root); if < 0, there are two complex roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.

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 the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert, complete the square on the quadratic expression.

Front

What is the significance of the leading coefficient (a) in a quadratic function?

Back

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