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Firlakuza [10]
3 years ago
13

Determine g(x+a)−g(x) for the following function. g(x)=4x2−6x

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

Answer:

8ax + (4a²- 6a)

Step-by-step explanation:

g(x)=4x²−6x

g(x+a)

= 4(x+a)² - 6(x+a)

= 4( x² + 2ax + a²) - 6x - 6a

= 4x² + (4)2ax + (4)a² - 6x - 6a

= 4x² + 8ax + 4a² - 6x - 6a

= 4x² + 8ax  - 6x + 4a²- 6a

= 4x² + (8a  - 6)x + (4a²- 6a)

g(x+a) - g(x)

= [4x² + (8a  - 6)x + (4a²- 6a)] - (4x²−6x)

=  4x² + (8a  - 6)x + (4a²- 6a) - 4x² + 6x

= (8a  - 6)x + (4a²- 6a) + 6x

= (8a  - 6 + 6)x + (4a²- 6a)

= 8ax + (4a²- 6a)

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Looking at y=-%285%2F2%29x we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-5%2F2 and the y-intercept is b=0 note: y=-%285%2F2%29x really looks like y=-%285%2F2%29x%2B0

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Now since the slope is comprised of the "rise" over the "run" this means

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and to the right 2 units to get to the next point  

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