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3 years ago

The graphs below have the same shape. What is the equation of the red

Mathematics

1 answer:

brilliants [131]3 years ago

6 0

Answer:

Option C is correct.

g(x) = x² + 4

Step-by-step explanation:

The image of the graph is missing from this qusstion, it was obtained and presented in the attached image to this answer.

Normally, f(x) = x²

And it is evident that g(x) is originally just given as g(x) = x²

But it has been moved along the y-axus to obtain what is available right now.

A vertical shift of magnitude c in a function is given as y + c = g(x) + c.

- If c is greater than 0, that is; positive, g(x) becomes g(x) + c

- If c is less than 0, that is; negative, g(x) becomes g(x) - c

And it is evident that the graph represented by the red line has moved up by 4 units, hence, the new function is given as

g(x) + 4 = x² + 4

Hope this Helps!!!

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What is the equation of this line in standard form? 8x−7y=−25 8x−9y=23 8x−9y=−23 9x−8y=23 Number graph ranging from negative fiv

Gnoma [55]

Answer:

The equation of line is:

$8x-9y=-23$

Step-by-step explanation:

We are given that a graph is a that passes through two points:

$(-4,-1)$ and $(\dfrac{1}{2},3)$

We know that the equation of line passing through two points:

$(a,b)$ and $(c,d)$ is given by:

$y-b=\dfrac{d-b}{b-a}\times (x-a)$

Here we have:

$(a,b)=(-4,-1)$ and $(c,d)=(\dfrac{1}{2},3)$

Hence, the equation of line is:

$y-(-1)=\dfrac{3-(-1)}{\dfrac{1}{2}-(-4)}\times (x-(-4))\\\\y+1=\dfrac{3+1}{\dfrac{1}{2}+4}\times (x+4)\\\\y+1=\dfrac{4}{\dfrac{9}{2}}\times (x+4)\\\\y+1=\dfrac{4\times 2}{9}\times (x+4)\\\\y+1=\dfrac{8}{9}\times (x+4)\\\\9\times (y+1)=8\times (x+4)\\\\9y+9=8x+8\times 4\\\\9y+9=8x+32\\\\8x-9y=9-32\\\\8x-9y=-23$