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An object is launched from a platform. Its height (in meters), x seconds after the launch, is modeled by h(x)=-5(x+1)(x-9) What is the height of the object at the time of launch? ◻ meters

An object is launched from a platform. \newlineIts height (in meters), xx seconds after the launch, is modeled by\newlineh(x)=−5(x+1)(x−9)h(x)=-5(x+1)(x-9)\newlineWhat is the height of the object at the time of launch?\newline □\square meters\text{meters}

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Full solution

Q. An object is launched from a platform. \newlineIts height (in meters), xx seconds after the launch, is modeled by\newlineh(x)=−5(x+1)(x−9)h(x)=-5(x+1)(x-9)\newlineWhat is the height of the object at the time of launch?\newline □\square meters\text{meters}
  1. Evaluate at x=0x=0: To find the height of the object at the time of launch, we need to evaluate the function h(x)h(x) at x=0x = 0, since the time of launch corresponds to the initial time, which is 00 seconds after the launch.
  2. Substitute x=0x=0: Substitute x=0x = 0 into the height function h(x)=−5(x+1)(x−9)h(x) = -5(x+1)(x-9).\newlineh(0)=−5(0+1)(0−9)h(0) = -5(0+1)(0-9)
  3. Perform multiplication: Perform the multiplication inside the parentheses.\newlineh(0)=−5(1)(−9)h(0) = -5(1)(-9)
  4. Find height at launch: Multiply the numbers together to find the height at the time of launch.\newlineh(0)=−5×1×−9h(0) = -5 \times 1 \times -9\newlineh(0)=45h(0) = 45

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