Projectile Motion and Quadratic Functions Quiz

Projectile Motion

• Projectile motion is the motion of an object influenced by gravity.
• The height of the object can be described by the following equation:
  • $h(t) = \frac{1}{2}at^{2} + V_{0}t + y_{0}$
    • Where:
      • $h(t)$ represents height
      • $t$ represents time
      • $a$ represents acceleration
      • $V_{0}$ represents initial velocity
      • $y_{0}$ represents initial height
• Zeros of a projectile equation represent the points where the object hits the ground (x-intercepts/roots).

Growing Steps Pattern

• The number of squares in each step follows a pattern:
  • Step 1: 1 square
  • Step 2: 4 squares
  • Step 3: 9 squares
• The equation $y = n^2$ describes the number of squares in the pattern, where 'n' represents the step number.

Quadratic Quiz

• Linear Functions
  • General form: $Ax + By = C$
  • Example: $y = 350 + 50m$
• Exponential Functions
  • General form: $y = ab^x$ or $y = a (1+r)^x$
• Quadratic Functions
  • General form: $y = ax^2 + bx + c$, $y = a(x - m)(x - n)$, or $y = a(x - h)^2 + k$
  • Example: $y = x^2$
• Parabolas
  • U-shaped curves whose direction depends on the value of 'a':
    • When 'a' is positive, the parabola opens upward ($∪$).
    • When 'a' is negative, the parabola opens downward ($∩$).
• Vertex of a Parabola
  • The minimum point of the parabola when 'a' is negative.
  • The maximum point of the parabola when 'a' is positive.

Measuring a Garden

• Noah has 50 meters of fencing to create a rectangular garden.
• Students are asked to:
  • Draw different rectangular garden shapes with varying lengths and widths.
  • Calculate the area of each rectangle.
  • Identify the length and width combination that results in the largest possible area.
  • Plot the length and area values on a coordinate plane to visualize the relationship.