The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is
.. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)
Using the vertex coordinates we read from the graph, the equation is
.. y = a*(x -2)^2 +1
We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0).
.. 0 = a*(1 -2)^2 +1
.. 0 = a*1 +1
.. -1 = a
Now we know the equation is
.. y = -(x -2)^2 +1
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If we like, we can expand it to
.. y = -(x^2 -4x +4) +1
.. y = -x^2 +4x -3
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An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as
.. y = a*(x -1)*(x -3)
Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get
.. 1 = a*(2 -1)*(2 -3) = a*1*-1 = -a
.. -1 = a
Then the equation of the graph can be written as
.. y = -(x -1)(x -3)
In expanded form, this is
.. y = -(x^2 -4x +3)
.. y = -x^2 +4x -3 . . . . . . same as above
Answer:
Step-by-step explanation:
a^2+ab+a
a(a+b+1)
C. Infinitely many of solutions
Answer: 2(34) + 2c = 98
Step-by-step explanation:
C = cost of one canteen
2 pair of boots at $ 34 each plus 2 canteens at (c) each totals $98.
2(34) + 2c = 98
68 +2c = 98. Subtract 68 from both sides. 68 - 68 +2c = 98 -68
2c = 30. Divide both sides by 2.
2c/2 = 30/2
c = 15 so each canteen costs $15
Check: 2 ($34) + 2 ($15) = $98
$68 + $30 = $98
$98 = $98
2C = 98
The appropriate selection is ...
D. x
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This is the purpose and meaning of an inverse function. Using inverse functions is the way we solve equations involving functions. They "undo" the effect of the function.
