4/11/2024 0 Comments Quadratic equation factored formWell, the key realization here is if you have a curve, if you have a parabola in Next question, how many secondsĪfter being launched will the rocket reach its maximum height? Pause the video again and see 18 seconds after launch, we see that our height is zero, we have hit the ground. You get x is equal to 18, so 18 seconds after launch, well we're going forward in time. Then this entire expression "could be equal to zero." X minus 18 equals zero, Then, we could also thinkĪbout, "Well, x minus 18 if "that's equal to zero, Number of seconds after the launch, so a negative When x is equal to negative two, but remember x is the To zero, then this equation would be satisfied. Well, negative four can't beĮqual to zero, so we could say x plus two equals zero. You get this to be equal to zero is if at least one of these three Of three different things being equal to zero, the way X equal to zero, so zero is equal to negative four times x plus two times x minus 18. To figure out the x when our height is equal to zero. Seconds after launch, how many seconds that's x, so we want The rocket to hit the ground? That means that the height isĮqual to zero, so if you want to figure out how many Launch will the rocket hit the ground? Pause this video again and This is going to be positive 72 times two, which is 144, so 144 meters. To be negative eight times negative 18, negativeĮight times negative 18, which is the same thing as negative eight times negative nine times two. Which is just going to be two times zero minus 18, To negative four, negative four times zero plus two, Just have to go back to this expression and replaceĪll the xs with zeros. "Well, what is h of zero?" To figure out h of zero, we X is equal to zero, they're essentially saying, Seconds after the launch, so at the time of launch, x Well, what is x at the time of launch? Well, x is the number of Now, the first thing theyĪsk us is what is the height of the rocket at the time of launch? Pause the video and see if Negative four times x plus two times x minus 18. Its height in meters, x secondsĪfter the launch is modeled by h of x is equal to Told a rocket is launched from a platform. So what you really are attempting to do is shift the whole thing 2 units to the left so that you will begin at (0,0) because you do not like the fact that it was launched from a platform. It not that the midpoint is 10 units from the y intercept, it is 10 units from the endpoint 18 and 18-10 = 8. While the -2 point is not within the domain of the word problem, it is still within the graph of the function and is the imaginary reflection of (18.0) which still gives midpoint at 8. The part between 16 and 18 just does not have a part that is reflected across the line of symmetry. Being launched from a platform that is 144 m about the ground gives a starting point at (0,144) not (0,0), and the symmetrical point would be at (16,144) which again gives the same midpoint at 8. So the word problem would cut off all of the parabola less than 0 (including the part that is reflected from 16-18 seconds at -2-0) as well as the part greater than 18. However, within the context of the word problem, the domain would be from 0 to 18 seconds when it hit the ground. If it were a function to be graphed independent of the word problem, both sides of the parabola would extend to negative infinity. In the problem, it clearly states that it is launched from a platform, so your assumption that it must start at 0 meters and 0 seconds is just incorrect. While I like your thinking process, you make several incorrect assumptions.
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