Question

jordan notices that the graph of the function h(x) is a vertical translation of the graph of the function g(x) shown 3 units. is jordan correct?
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g(x) = (x - 3)²
h(x) = (x - 3)² + 3

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jordan is choose.... the function h(x) can be written as choose..., which represents a vertical choose... 3 units.

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) \), the transformation \( y = f(x)+k \) shifts the graph vertically. If \( k>0 \), it's a shift up by \( k \) units; if \( k<0 \), it's a shift down by \( |k| \) units.

Step2: Analyze \( g(x) \) and \( h(x) \)

Given \( g(x)=(x - 3)^2 \) and \( h(x)=(x - 3)^2+3 \). Comparing to the vertical shift formula, \( h(x)=g(x)+3 \).

Step3: Determine Correctness

Since \( h(x) \) is \( g(x) \) shifted up 3 units (vertical shift), Jordan's statement is correct.

Answer:

Jordan is correct. The function \( h(x) \) can be written as \( g(x)+3 \), which represents a vertical shift up 3 units.