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3 years ago

Consider the function ƒ(x) = (x + 1)2 – 1. Which of the following functions stretches ƒ(x) vertically by a factor of 4?

Mathematics

1 answer:

laila [671]3 years ago

5 0

Answer:

C f(x) = 4(x+1)2-1

Step-by-step explanation:

factor of 4 = 2^2

(x+1)2-1 = 4(x+1) 2-1 = with x

= 4(+1) 2-1 = without x

= (4 - 4) 2 = individual products of -1

= (8 - 8 ) = individual products of 2

= 8 - 8 = 2^2 -2^2

= 2^2 - 2^2

(x+1)2-1 = 4(x+1)2-1 = with x

= 2x^2 -2^2

-x = 2^2 -2^2

x = -2^2-2^2

x = 4

which proves f(x) is a factor of 4

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F(x)=-x^2+8x+15 ...?

rusak2 [61]

Here i how I would do it:f(x)=−x2+8x+15
set f(x) = 0 to find the points at which the graph crosses the x-axis. So−x2+8x+15=0
multiply through by -1x2−8x−15=0 (x−4)2−31=0 x=4±31−−√
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through(0,15),(4−31−−√,0)and(4+31−−√,0)
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:f(x)=31−(x−4)2
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.

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