Question

This question has two parts. First, answer Part 1. Then, answer Part 2.

Consider function f(x)=(x-3)(x+1).


Part 1

It point (1-p,y) belongs to the graph of the function, which point must also belong to the graph?

A. (p-1,y)

B. (1+p,y)

C. (-1-p,y)

D. (y,1-p)


Part 2

If x=a is the line of symmetry of the function, what is the value of a? (use only the digits 0-9 and the decimal point and the negative sign, if needed, to write the number)

Answer 1

1. B. (1+p,y)
2. 1

Explanation:

The line of symmetry is halfway between the zeros, so is found at ...

x = (3 -1)/2 = 1

Part 1

If point (1-p, y) is on the graph, so is the point that is its reflection in the line of symmetry: (2 -(1-p), y) = (1+p, y).

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Part 2

If x=a is the line of symmetry, a=1, since x=1 is the line of symmetry as found above.

_____

Comment on midpoint & line of symmetry

If M is the midpoint between A and B, then ...

M = (A+B)/2

B = 2M -A . . . . solve for B

The reflection of a point (x, y) in the line x=a will be (2a-x, y). That is where the "2" comes from in the equation used in part 1.