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let h(x)=x2+kx−4h(x)=x^2+kx-4. If h(−3)=−7h(-3)=-7 , what is the value of h(2)h(2)

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Full solution

Q. let h(x)=x2+kx−4h(x)=x^2+kx-4. If h(−3)=−7h(-3)=-7 , what is the value of h(2)h(2)
  1. Calculate kk: Calculate h(−3)h(-3) to find kk:h(−3)=(−3)2+k(−3)−4=9−3k−4=5−3k.h(-3) = (-3)^2 + k(-3) - 4 = 9 - 3k - 4 = 5 - 3k.Set h(−3)=−7h(-3) = -7: 5−3k=−7.5 - 3k = -7.Solve for kk: −3k=−7−5-3k = -7 - 5, −3k=−12-3k = -12, k=4.k = 4.
  2. Substitute kk into h(x)h(x): Substitute k=4k = 4 into h(x)h(x) and calculate h(2)h(2):\newlineh(x)=x2+4x−4.h(x) = x^2 + 4x - 4.\newlineh(2)=(2)2+4(2)−4=4+8−4=8.h(2) = (2)^2 + 4(2) - 4 = 4 + 8 - 4 = 8.

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