Question 1: Solve for x: 2x^2 + 5x - 3 = 0 using the quadratic formula.

Answer: x = 0.5 or x = -3

Question 2: Find the roots of x^2 - 4x + 4 = 0.

Answer: x = 2

Question 3: Determine the solutions to 3x^2 + 2x - 1 = 0 and verify using the quadratic formula.

Answer: x = (1/3) or x = -1

Question 4: Plot the graph of y = -x^2 + 4x - 3 and identify the x-intercepts.

Answer: x = 1 or x = 3

Question 5: A quadratic equation x^2 + bx + 6 = 0 has one real root. Find b.

Answer: b = ±2√6

Question 6: Solve the quadratic equation 4x^2 - 12x + 9 = 0 and explain why the roots are equal.

Answer: x = 1.5; both roots are equal because discriminant = 0

Question 7: A rectangular garden's length is modeled by 2x + 3, and its width by x. The area is 40 square meters. Find x and the dimensions.

Answer: x = 4; length = 11, width = 4

Question 8: Construct a quadratic with roots at x = -1 and x = 3. Write the equation.

Answer: x^2 - 2x - 3 = 0

Question 9: Identify and correct the mistake in solving 5x^2 + 2x + 1 = 0 if a student claims the solutions are x = 1 and x = -0.2.

Answer: Mistake: Incorrectly solving without using the quadratic formula; solutions are complex, not real.

Question 10: Solve 6x^2 + 11x - 35 = 0 and classify the roots as real and distinct, real and equal, or complex.

Answer: x = 3 or x = -35/6; roots are real and distinct

Question 11: A problem states: 'Find the quadratic equation if roots are 2 and -5.' Verify the roots by solving the quadratic equation you constructed.

Answer: Equation: x^2 + 3x - 10 = 0; solutions at x=2 and x=-5