Question

I need help on this formative

The graph of the parent quadratic
function is f(x) = x2.

How does that graph transform to the function below?

g(x)=-(x-6)^2

Narrower

Wider

Reflected across the x-axis

Translated / Shifted Up

Translated / Shifted Down

Translated / Shifted Left

Translated / Shifted Right

Answer 1

• Reflected across the x-axis
• Translated / Shifted Right

Explanation:

You want the transformation that get you from f(x) = x² to g(x) = -(x -6)².

Transformation

The attachment shows both functions.

The leading minus sign causes the graph to be reflected across the x-axis.

Replacing x with (x -6) causes the graph to be shifted right (translated) 6 units.

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Additional comment

If there were any horizontal or vertical scaling, the graph would become wider or narrower. There is no scaling here, so the graph retains its original width.

Vertical expansion by a factor of k would make the graph narrower for k > 1:

g(x) = kx²

Horizontal expansion by a factor of k would make the graph wider for k > 1.

g(x) = (x/k)²