The problem in the uploaded image involves the equation $h = 5t(5-t)$, which models the height of a stone thrown vertically upwards as a function of time $t$. Let's summarize and analyze the tasks mentioned:

1. Interpret the equation:
   $h = 5t(5-t)$, where:

   • $h$: height (in cm).
   • $t$: time (in seconds).

   Simplified, $h = 25t - 5t^2$, which is a quadratic equation.

2. Tasks listed:

   • a) Calculate values of $h$ for $t = 0, 1, 2, 3, 4, 5, 6$.
   • b) Plot the graph of $h$ against $t$, using appropriate scales on the axes.
   • c) Use the graph to:
     • Find when $h = 0$ (stone hits the ground).
     • Determine the time when the stone is 25 cm above the ground.

Let's calculate the values for part (a) first:

Calculations:

Given $h = 5t(5-t) = 25t - 5t^2$:

• For $t = 0$: $h = 25(0) - 5(0)^2 = 0$.
• For $t = 1$: $h = 25(1) - 5(1)^2 = 25 - 5 = 20$.
• For $t = 2$: $h = 25(2) - 5(2)^2 = 50 - 20 = 30$.
• For $t = 3$: $h = 25(3) - 5(3)^2 = 75 - 45 = 30$.
• For $t = 4$: $h = 25(4) - 5(4)^2 = 100 - 80 = 20$.
• For $t = 5$: $h = 25(5) - 5(5)^2 = 125 - 125 = 0$.
• For $t = 6$: $h = 25(6) - 5(6)^2 = 150 - 180 = -30$ (not meaningful in this context).

Do you want me to plot the graph for part (b) and analyze part (c)? Let me know!

Follow-Up Questions:

1. Would you like an explanation of how to choose the axes and scales for the graph?
2. Should I clarify how to interpret when the stone reaches 25 cm using the graph?
3. Do you need a detailed explanation of the quadratic equation and its symmetry?
4. Would you like help verifying how to find roots of the equation $h = 0$ algebraically?
5. Should I generate the graph for you with proper annotations?

Tip: The symmetry of quadratic equations can help simplify calculations when analyzing motion.