Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Identify the values of a, b, and c in the equation: 3x² - 12x + 9.

Back

a = 3, b = -12, c = 9.

Front

What does the 'discriminant' in the quadratic formula indicate?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve for x using the quadratic formula: 2x² + 4x - 6 = 0.

Back

x = 1, -3.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the axis of symmetry for a quadratic equation?

Back

The axis of symmetry can be found using the formula 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

Solve the quadratic equation: x² - 4x - 5 = 0.

Back

x = 5, -1.

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.

Front

Identify the 'c' value in the equation: y = 5x² + 3x + 7.

Back

c = 7.