Question

What transformation converts the graph of
()=−9(−7)2+9 to ()−9(−7)2+6?

Answer 1

The given transformation is a vertical shift downward by 3 units.

Explanation:

The transformation mentioned in the question involves changing the original function
`\(f(x)=-9(x+7)^2+9\) to \(g(x)=-9(x+7)^2+6\)`. To understand this transformation, let's analyze the change in the constant term. In the original function,
`\(f(x)=-9(x+7)^2+\underline{9}\)` , the constant term is 9. In the transformed function,
`\(g(x)=-9(x+7)^2+\underline{6}\)`, the constant term is now 6. This represents a vertical shift downward by 3 units. The subtraction of 3 from the original constant term results in a lower positioning of the graph along the y-axis.

In mathematical terms, the general form of a quadratic function
`\(ax^2+bx+c\)` involves a term (c) that dictates the vertical position of the parabola. Changing this term directly influences the vertical shift. In our case, subtracting 3 from the constant term in the original function causes the entire graph to shift downward by 3 units. This understanding aligns with the broader concept of transformations in functions, where alterations in coefficients or constants lead to predictable changes in the graph's appearance.