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1. The distance d from p to the origin as a function of x is;  d = √(x⁴ + 17x² + 64)

   How to use Pythagoras Theorem?

   This question uses the Pythagorean Theorem to determine the length of a hypotenuse of a right triangle.

   The base of the triangle goes x distance along the x-axis, then y distance up to the point in question.  

   In order to find the distance (the hypotenuse of that triangle) as a function of x, we need two points.

   Point P = (x , x² + 8)

   Point 2 = (0, 0)

   The formula for distance is;

   d = √[(xP – x²)² + (yP – y²)²]

   Plugging in the relevant Values gives;

   d = √[(x – 0)² + (x² + 8 – 0)²]

   d = √[x² + (x⁴ + 16x² + 64)]

   d = √(x⁴ + 17x² + 64)

   Thus, the distance d from p to the origin as a function of x is;  d = √(x⁴ + 17x² + 64)

   Complete Question is;

   Let P = (x, y) be a point on the graph of y = x² + 8. Express the distance d from p to the origin as a function of x.

   Read more about Pythagoras Theorem at; https://brainly.com/question/654982

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