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A cubic function has the rule f(x) = a (x-h)^3 +7. The graph of the function passes through the points (4,7) and (5,10). Find the values of a and h, thus the equation. Please provide a full working out! Thankssssss :D

Respuesta :

sqdancefan

Answer:

  • a = 3
  • h = 4
  • f(x) = 3(x -4)³ +7

Step-by-step explanation:

You want the values of 'a' and 'h' so that the points (4, 7) and (5, 10) will lie on the graph of f(x) = a(x -h)³ +7.

Equations

Substituting for x and f(x) gives two equations in the two unknowns:

  7 = a(4 -h)³ +7

  10 = a(5 -h)³ +7

Solution

Subtracting 7 from each equation, we get ...

  0 = a(4 -h)³ . . . . h = 4 . . . . . . . value that makes (4-h) = 0

  3 = a(5 -4)³ . . . . a = 3 . . . . . . . use the value of h we found

The values of a and h are 3 and 4, respectively. The equation for f(x) is ...

  f(x) = 3(x -4)³ +7

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