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9966 [12]
3 years ago
6

2y+ 18x = 2x(x +9) Please show work!

Mathematics
1 answer:
Levart [38]3 years ago
4 0

Answer:

Step-by-step explanation:

2y+18x=2x\left(x+9\right)\\Parabola\:standard\:equation\\4p\left(yk\right)=\left(xh\right)^2\:\mathrm{\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:parabola\:with\:vertex\:at}\:\left(h,\:k\right), \\\mathrm{and\:a\:focal\:length\:}\:|p|\\\mathrm{Rewrite}\:2y+18x=2x\left(x+9\right)\:\mathrm{in\:the\:standard\:form}\\2y+18x=2x\left(x+9\right)\\\mathrm{Rewrite\:as}\\2y=2x\left(x+9\right)-18x\\\mathrm{Divide\:by}\:2\\y=x^2\\\mathrm{Rewrite\:in\:standard\:form}4\cdot \frac{1}{4}\left(y-0\right)=\left(x-0\right)^2\\Therefore\:parabola\:properties\:are:\\\left(h,\:k\right)=\left(0,\:0\right),\:p=\frac{1}{4}

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Therefore the new coordinate of the point is (2,-4)

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4 years ago
30 POINTS!! WILL VOTE BRAINIEST
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Part A:

Consider from x = -5 to x = -4, they are 1 unit apart and the difference of their outputs is given by:

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Part B:

Consider from x = -3 to x = -1, they are 2 units apart and the difference of their outputs is given by:

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Thus, the value of the output increases by 16 units for each two units increase in the input.



Part C:

Consider from x = 0 to x = 3, they are 3 units apart and the difference of their outputs is given by:

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Thus, the value of the output increases by 24 units for each three units increase in the input.



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It can be noticed that the ratio difference in the outputs to the input intervals are equal for all the given input intervals.

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