This is the sketch of the graph y=(x-1)(x+3)

  A(1, 0), B(3, 0), P(0, 3), Q(2, -1)

Step-by-step explanation:

Points A and B are the x-intercepts of the graph. The values of x at those points are values that make the value of y be zero. The zero product rule tells you these must be the values that make the factors of y = 0.

  x -1 = 0   ⇒   x = 1

  x -3 = 0   ⇒   x = 3

This means ...

  A = (1, 0)

  B = (3, 0)

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The value of y at the y-intercept is the value when x=0:

  y = (0 -1)(0 -3) = 3

  P = (0, 3)

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The x-coordinate of the vertex is on the line of symmetry, halfway between the x-intercepts.

  Qx = (1 +3)/2 = 2

The y-coordinate of the vertex is the value of y for that value of x.

  y = (2 -1)(2 -3) = (1)(-1) = -1

The coordinates of Q are ...

  Q = (2, -1)

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Additional comment

A graphing calculator can help you with questions like this.

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

range is infinite on both x and y axis positive and negative

step-by-step explanation: