The functions f(x)=x^2 and g(x)=(1)/(2)(x-5)^2 are graphed on the same coordinate grid.Which statements are true? Select THREE correct answers. A. The graph of g is a vertical compression of the graph off. B. The graph of is a vertical stretch of the graph off. C. To create g f is translated 5 units to the left. D. To create g f is translated 5 units to the right. E. The vertex ofg is 3 units to the left of the vertex off. F. The vertex ofg is 5 units to the right of the vertex of f.

Question

The functions f(x)=x^2 and g(x)=(1)/(2)(x-5)^2 are graphed on the same coordinate grid.Which statements are true? Select THREE correct answers. A. The graph of g is a vertical compression of the graph off. B. The graph of is a vertical stretch of the graph off. C. To create g f is translated 5 units to the left. D. To create g f is translated 5 units to the right. E. The vertex ofg is 3 units to the left of the vertex off. F. The vertex ofg is 5 units to the right of the vertex of f.

Answer 1

To determine which statements are true, we need to analyze the given functions and their graphs.Step 1: Analyze the function

The function

is a basic quadratic function. Its graph is a parabola that opens upwards with its vertex at the origin (0,0).Step 2: Analyze the function

The function

is a transformed quadratic function. The term

indicates a horizontal translation of 5 units to the right, and the coefficient

indicates a vertical compression by a factor of

.Step 3: Compare the graphs of

and

Based on the analysis in steps 1 and 2, we can conclude the following:- The graph of

is a vertical compression of the graph of

by a factor of

.- The graph of

is translated 5 units to the right compared to the graph of

.- The vertex of

is 5 units to the right of the vertex of

.Therefore, the correct answers are:A. The graph of g is a vertical compression of the graph off.D. To create g f is translated 5 units to the right.F. The vertex ofg is 5 units to the right of the vertex of f.

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