Assessment Questions

1. Graph \( y = x^2 - 4x + 3 \). State the vertex, axis of symmetry, and intercepts.
2. Solve by factoring: \( x^2 - 7x + 12 = 0 \).
3. Solve using the quadratic formula: \( 2x^2 + 3x - 5 = 0 \).
4. Complete the square: \( x^2 + 6x + 5 = 0 \).
5. Projectile problem: A rock is thrown upward with \( h(t) = -5t^2 + 25t + 2 \). Find maximum height and time of flight.
6. Revenue function: \( R(x) = -2x^2 + 60x \). Find number of units that maximizes revenue and the maximum revenue.
7. Word problem: The product of two consecutive integers is 56. Find the integers.
8. Mixed practice: Solve \( 3x^2 - 12x = 0 \).
9. Graphing: Sketch \( y = -x^2 + 4x \). Identify its vertex and axis of symmetry.
10. Real-life application: A rectangle has area modeled by \( A(x) = x(30 - x) \). Find dimensions that maximize the area.