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

Identify a, b, and c in the equation: 4x² - 8x - 3 = 0

Back

a = 4, b = -8, c = -3.

Front

Identify a, b, and c in the equation: x² - 6x + 14 = 0

Back

a = 1, b = -6, c = 14.

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant determines the nature of the roots of the quadratic equation: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve using the Quadratic Formula: 2x² + x - 4 = 0

Back

x = 1.19 and x = -1.69.

Front

Solve: 2x² + 7x - 15 = 0

Back

x = -5 or x = 1.5.

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 represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line that divides the parabola into two mirror images, given by 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 > 0, it opens upwards; if a < 0, it opens downwards.