Fit a quadratic function to these three points: (−2, 8), (0, −4), and (4, 68) y = −2x2 + 2x − 4 y = 4x2 + 2x − 4 y = −2x2 − 2x −
4 y = −4x2 − 2x − 4
1 answer:
Answer:
y = 4x² + 2x − 4
Step-by-step explanation:
The y-values go down and up again, so the parabola opens upward. That means the x² coefficient must be positive. All answer choices are eliminated except one.
y = 4x² +2x -4
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There are other ways to get the answer. One of them is to use the quadratic regression function of a spreadsheet or graphing calculator. The one attached shows the points are matched by the equation ...
y = 4x² +2x -4 . . . . . as above
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The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars (not all zero) such that
which leads to the system of linear equations,
From the third equation, we have , and substituting this into the second equation gives
and in turn, . Substituting these into the first equation gives
which tells us that any value of will work. If
, then
and
. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.