Question

Can anyone lend a hand with some Algebra? Thank you!

Answer 1

Answer: g(x) = (x - 3)² - 3

Explanation:

f(x) = x²

= (x - 0)² + 0

This is comparable to the equation f(x) = (x - h)² + k where h represents the shift to the right and k represents the shift up.

So, 3 to the right means h = 3. 3 down means k = -3

g(x) = [x - (3)]² + (-3)

= (x - 3)² - 3

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Answer:
`\bold{-(4x+101)/(8)}`

Explanation:

`2\bigg((x)/(2)-5\bigg)-(3)/(2)\bigg(x+(7)/(4)\bigg)`

`=2\bigg((x)/(2)\bigg)-2(5) - (3)/(2)(x)-(3)/(2)\bigg((7)/(4)\bigg)`

`=(2)/(2)x - 10 - (3)/(2)x-(21)/(8)`

`=(2)/(2)x - (80)/(8) - (3)/(2)x-(21)/(8)`

`=(2)/(2)x - (3)/(2)x-(21)/(8)- (80)/(8)`

`=(-1)/(2)x -(101)/(8)`

`=(-4)/(8)x -(101)/(8)`

`=(-4x-101)/(8)`

`=-(4x+101)/(8)`