Quadratic Formula

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 (b² - 4ac) indicate?

Back

The discriminant determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8

Back

x = -8 or 4.

Front

What is the first step in using the Quadratic Formula?

Back

Rearrange the equation to the standard form ax² + bx + c = 0.

Front

Solve using the Quadratic Formula: 2x² + 7x - 15 = 0

Back

x = -5 or 3/2.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 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

How do you find 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 significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

Solve using the Quadratic Formula: 9x² = 4 + 7x

Back

x = 1/3 or -4.