Quadratic Formula Practice

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (b² - 4ac) indicate in a quadratic equation?

Back

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

Front

Solve for x: x² + 6x + 9 = 0

Back

x = -3 (double root).

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

How do you complete the square for the equation x² + 4x = 5?

Back

Add (4/2)² = 4 to both sides: (x + 2)² = 9, then x + 2 = ±3.

Front

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

Back

x = 3 and x = -1.

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

What is the axis of symmetry for the quadratic equation y = x² - 4x + 3?

Back

The axis of symmetry is x = -b/(2a) = 2.

Front

Solve for x: 3x² + 12x + 12 = 0

Back

x = -2 (double root).

Front

What is the effect 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.