Trình bày nội dung của phương pháp bình phương bé nhất. Phân biệt phương pháp
1 answer:
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The point-slope form of the equation of a line is
where
is a point on the line, and
is the slope of the line.
We can use either one of the two given points as the point on the line.
We also need to find the slope. We can use the coordinates of the two given points to find the slope of the line.
The slope of the line that passes through points
and 
is
Let's find the slope using (-3, 5) as point 1 and (-1, 4) as point 2.
Now we use the point-slope formula with point 1 and the slope we found just above.
where
is a point on the line, and
is the slope of the line.
We can use either one of the two given points as the point on the line.
We also need to find the slope. We can use the coordinates of the two given points to find the slope of the line.
The slope of the line that passes through points
is
Let's find the slope using (-3, 5) as point 1 and (-1, 4) as point 2.
Now we use the point-slope formula with point 1 and the slope we found just above.
Answer:
Please see attached image for the graph
Step-by-step explanation:
To graph the elevation versus time, we start by plotting the first point at time zero (when the climb begins) when Zane is 20 meters below the edge (-20 meters). This corresponds to the point (0, -20).
One second later (1 in the horizontal axis), Zane has moved up 4 meters, now reaching -16 meters. This is the point (1, -16) on the graph.
One second later at time 2 seconds, he is another 4 meters up which corresponds to the point (2, -12) on the graph.
you can go on like this plotting more points on the graph.
Please see the attached image that illustrates this and shows the appropriate line that represents Zane's position versus time (pictured in red)
Answer:
"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the -coordinate of the quadratic function, and then substituting that value into the function."
Step-by-step explanation:
Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a <em>polynomial</em> of degree 2, which is a fancy way of saying that something is a quadratic), the -coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.
In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve , which gives
(the 'V' stands for 'or'). We can take the average of the two roots to get the
-coordinate of the minimum point of the graph (which, in this case, is
).
Having the -coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the
-coordinate of the extremum.