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find the equation of a quadratic function with the ordered pairs (4,5)(4,5) and (5,2)(5,2)

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Full solution

Q. find the equation of a quadratic function with the ordered pairs (4,5)(4,5) and (5,2)(5,2)
  1. Identify Quadratic Form: Identify the general form of a quadratic equation.\newlineA quadratic equation can be written as y=ax2+bx+cy = ax^2 + bx + c.
  2. Set Up Equations: Set up equations using the given points.\newlineSubstitute (4,5)(4,5) into the quadratic equation:\newline5=a(4)2+b(4)+c5 = a(4)^2 + b(4) + c\newline5=16a+4b+c5 = 16a + 4b + c
  3. Substitute Points: Substitute (5,2)(5,2) into the quadratic equation:\newline2=a(5)2+b(5)+c2 = a(5)^2 + b(5) + c\newline2=25a+5b+c2 = 25a + 5b + c
  4. Solve System of Equations: Solve the system of equations to find aa, bb, and cc. From the equations: 16a+4b+c=516a + 4b + c = 5 25a+5b+c=225a + 5b + c = 2 Subtract the first equation from the second: (25a+5b+c)−(16a+4b+c)=2−5(25a + 5b + c) - (16a + 4b + c) = 2 - 5 9a+b=−39a + b = -3
  5. Need Additional Information: We need a third point or additional information to solve for aa, bb, and cc uniquely.\newlineCurrently, we have two equations but three unknowns, which is insufficient to find a unique solution.

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