Mastering Quadratic Equations

What is the quadratic formula?

• x = (b ± √(b² - 2ac)) / (a)

• x = (b ± √(b² + 4ac)) / (2a)

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (-b ± 2√(b² - 4ac)) / (2a)

Solve for x: 2x² - 4x - 6 = 0

• x = 3, x = -1

• x = 4

• x = 2

• x = 0

What are the values of a, b, and c in the equation x² + 5x + 6 = 0?

• a = 1, b = 6, c = 5

• a = 0, b = 5, c = 6

• a = 2, b = 3, c = 4

• a = 1, b = 5, c = 6

How many solutions can a quadratic equation have?

• Only 1 solution

• 3 solutions

• Infinitely many solutions

• 0, 1, or 2 solutions

Solve for x: x² - 3x + 2 = 0 using the formula method.

• x = 0, 3

• x = -1, 4

• x = 1, 3

• x = 1, 2

What does the discriminant tell you about the roots?

• The discriminant shows the average of the roots.

• The discriminant indicates the sum of the roots.

• The discriminant reveals the product of the roots.

• The discriminant tells you the nature of the roots: two distinct real roots, one real root, or two complex roots.

If the discriminant is negative, what can you say about the solutions?

• The solutions are always positive.

• The solutions are complex (imaginary) and not real.

• The solutions are real and equal.

• The solutions are real and distinct.

Solve for x: 3x² + 12x + 12 = 0 using the quadratic formula.

• x = -2

• x = 1

• x = -3

• x = 0

What is the vertex form of a quadratic equation?

• y = a(x - h)² + k

• y = ax² + bx + c

• y = a(x - h) + k

• y = a(x + h)² - k

How do you determine if a quadratic opens upwards or downwards?

• The direction is determined by the value of 'c' in the equation.

• A quadratic always opens downwards regardless of its coefficients.

• The direction of a quadratic is determined by the sign of the coefficient 'a' in the equation ax² + bx + c.

• The quadratic opens upwards if the coefficient 'b' is positive.