Question

How does the graph of y = a(x – h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. The vertex of the graph moves to a point half as far from the x-axis. The vertex of the graph moves to a point half as far from the y-axis.

Answer 1

Answer:

The vertex of the graph moves to a point twice as far from the y-axis.

Step-by-step explanation:

How does the graph of y = a(x – h)2 + k change if the value of h is doubled?

The vertex of the graph moves to a point twice as far from the x-axis.

The vertex of the graph moves to a point twice as far from the y-axis.

because the role of h is to indicate the distance of the vertex from the y-axis.

The vertex of the graph moves to a point half as far from the x-axis.

The vertex of the graph moves to a point half as far from the y-axis.

Answer 2

Transformation involves changing the position of a function.

When h is doubled in $\mathbf{y = a(x - h)^2 + k}$, the vertex of the graph moves to a point twice as far from the y-axis.

The function is given as:

$\mathbf{y = a(x - h)^2 + k}$

When the value of h is doubled, the new function becomes:

$\mathbf{y' = a(x - 2h)^2 + k}$

Rewrite as:

$\mathbf{y' = a(x - h- h)^2 + k}$

The above equation means that:

Function y will be translated to the right by h units

Assume the vertex is:

$\mathbf{Vertex = (2,5)}$

The new vertex will be:

$\mathbf{Vertex = (4,5)}$

Comparing the vertices, it means that:

The new function will have its vertex twice as far from the y-axis

Hence, option (b) is correct.

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