Quadratic Formula

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) indicate?

Back

The discriminant determines the nature of the roots of a quadratic equation: if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is a quadratic equation?

Back

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

Front

How do you convert a quadratic equation to standard form?

Back

To convert to standard form, rearrange the equation to the form ax² + bx + c = 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.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) 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 x = -b/(2a).

Front

What is the significance of the 'a' value in a quadratic equation?

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (px + q)(rx + s) = 0 and set each factor to zero.

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

The sum of the roots is -b/a and the product of the roots is c/a.