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# Seraphin is comparing the graphs of the parent function y = x2 and the function y = 6(x − 3)2

Seraphin is comparing the graphs of the parent function y = x2 and the function y = 6(x − 3)2 − 8. He makes the following statements about the new function.

• Stretch vertically by a factor of 6.

• Translate 3 units right.

• Translate 8 units up.

Are Seraphin’s statements correct? Explain why or why not.

No; Seraphin’s first statement is not correct. Because the a-value is positive, the graph should be stretched horizontally by a factor of 6.

No; Seraphin’s third statement is not correct. Because the c-value is positive, the graph should be translated 3 units to the left.

No; Seraphin’s third statement is not correct. Because the d-value is negative, the graph should be translated 8 units down.

Yes; the statements are all correct.