The function provided is $h(t) = t^2 - 2t$.

Let's solve the given parts one by one:

(a) $h(2)$

Substitute $t = 2$ into the function: $h(2) = (2)^2 - 2(2) = 4 - 4 = 0$

(b) $h(-1)$

Substitute $t = -1$ into the function: $h(-1) = (-1)^2 - 2(-1) = 1 + 2 = 3$

(c) $h(x + 2)$

Substitute $t = x + 2$ into the function: $h(x + 2) = (x + 2)^2 - 2(x + 2)$ Expanding this: $h(x + 2) = (x^2 + 4x + 4) - 2(x + 2) = x^2 + 4x + 4 - 2x - 4$ Simplifying: $h(x + 2) = x^2 + 2x$

(d) $h(1.5)$

Substitute $t = 1.5$ into the function: $h(1.5) = (1.5)^2 - 2(1.5) = 2.25 - 3 = -0.75$

Summary of Answers:

• (a) $h(2) = 0$
• (b) $h(-1) = 3$
• (c) $h(x + 2) = x^2 + 2x$
• (d) $h(1.5) = -0.75$

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. Find $h(0)$ for the same function.
2. Calculate the derivative $h'(t)$ of the function.
3. Find the roots of the equation $h(t) = 0$.
4. Evaluate $h(x-3)$ and simplify the expression.
5. Determine the vertex of the parabola represented by $h(t)$.

Tip: When substituting expressions into a function, be sure to simplify carefully to avoid errors.