Question

Which is one of the transformations applied to the graph of title="f(x)=x^2" alt="f(x)=x^2" align="absmiddle" class="latex-formula"> to produce the graph of $p(x)=-50+14x-x^2$?
A. a shift down 1 unit

B. a shift left 7 units

C. a shift right 1 unit

D. a shift up 7 units


Could you explain your answer?


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-Charlie

Answer 1

Answer:

A

Step-by-step explanation:

Write each parabola in standard form.

f(x) = x²

f(x) = (x − 0)² + 0

For p(x), complete the square.

p(x) = -50 + 14x − x²

p(x) = -(x² − 14x + 50)

p(x) = -(x² − 14x + 49 + 1)

p(x) = -(x² − 14x + 49) − 1

p(x) = -(x − 7)² − 1

The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.

The answer is A.