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:
B ------- DE ≅ RS
it's B because DE and RS both contain the equal angles.
Answer:
1
Step-by-step explanation:
2x + 9 - 17x - 15 - x =????
2x - 17x - x + 9 - 15 = 0
- 15x - x - 16 = 0
- 16x - 16 =0
-16x = 16
x = 16 / - 16
x = 1
Answer:
x⁴ + 2 x² + 1
Step-by-step explanation:
given solution of the polynomial
i, −i, 1, −1.
equation of the polynomial will be equal to
=(x - i)(x + i)(x - 1)(x + 1)
= (x² + i x - i x - i²)(x² + x - x + 1)
=(x² - (-1))(x² + 1 )
= (x² + 1)(x² + 1)
= x⁴ + x² + x² + 1
= x⁴ + 2 x² + 1
hence, the required polynomial equation is x⁴ + 2 x² + 1