Questions: a. Use a graphing utility to graph (y=x^2-73 x+700) in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic function. c. Find a viewing rectangle that will give a relatively complete picture of the parabola. d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola. a. What do you observe in the standard viewing rectangle? b. The coordinates of the vertex are . (Type an ordered pair.)

Solution Steps

• Use a graphing utility to graph the function \( y = x^2 - 73x + 700 \) in a standard viewing rectangle.
• Observe the graph to understand its shape and key features.

• The vertex of a quadratic function \( y = ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \).
• For the given function \( y = x^2 - 73x + 700 \):
  • \( a = 1 \)
  • \( b = -73 \)
  • \( x = -\frac{-73}{2 \cdot 1} = \frac{73}{2} = 36.5 \)
• Substitute \( x = 36.5 \) back into the function to find the y-coordinate:
  • \( y = (36.5)^2 - 73 \cdot 36.5 + 700 \)
  • \( y = 1332.25 - 2664.5 + 700 \)
  • \( y = -632.25 \)
• Therefore, the vertex is \( (36.5, -632.25) \).

• To get a relatively complete picture of the parabola, choose a viewing rectangle that includes the vertex.
• Since the vertex is at \( (36.5, -632.25) \), a suitable viewing rectangle might be \( [0, 50] \) for the x-axis and \( [-700, 0] \) for the y-axis.

Final Answer