The graph of ℎ is obtained when 𝑓(𝑥) =− 3𝑥 is reflected along the 2 + 12 line 𝑦 = 0. Write down the equation of ℎ in the form ℎ(𝑥) = 𝑝𝑥 2 + 𝑘.

Let's break down the problem step-by-step:

1. **Given Function**: We start with \( f(x) = -3x \).
2. **Reflection Line**: The reflection line is \( y = 0 \), which is the x-axis.
   
3. **Reflection of \( f(x) \) Along the x-axis**:
   - When we reflect \( f(x) = -3x \) across the x-axis, we change the sign of \( f(x) \).
   - The reflection of \( f(x) = -3x \) across \( y = 0 \) is \( h(x) = 3x \).

4. **Writing \( h(x) \) in the Given Form**: 
   - We want \( h(x) \) in the form \( h(x) = px^2 + k \).
   - Since \( h(x) = 3x \) is a linear function, \( p = 0 \) and \( h(x) \) simplifies to a constant term, \( h(x) = 3x \).

**Final Answer**:
\[
h(x) = 3x

The graph of ℎ is obtained when 𝑓(𝑥) =− 3𝑥 is reflected along the line 𝑦 = 0. Write down the equation of ℎ in the form ℎ(𝑥) = 𝑝𝑥^2 + 𝑘.

Learn how to find the equation of h(x) by reflecting the linear function f(x) = -3x across the x-axis. This problem covers algebraic concepts including reflections and linear functions, suitable for students in Grades 9-10.

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