Answer: g(x) = (x - 3)² - 3
Step-by-step 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: [tex]\bold{-\dfrac{4x+101}{8}}[/tex]
Step-by-step explanation:
[tex]2\bigg(\dfrac{x}{2}-5\bigg)-\dfrac{3}{2}\bigg(x+\dfrac{7}{4}\bigg)[/tex]
[tex]=2\bigg(\dfrac{x}{2}\bigg)-2(5) - \dfrac{3}{2}(x)-\dfrac{3}{2}\bigg(\dfrac{7}{4}\bigg)[/tex]
[tex]=\dfrac{2}{2}x - 10 - \dfrac{3}{2}x-\dfrac{21}{8}[/tex]
[tex]=\dfrac{2}{2}x - \dfrac{80}{8} - \dfrac{3}{2}x-\dfrac{21}{8}[/tex]
[tex]=\dfrac{2}{2}x - \dfrac{3}{2}x-\dfrac{21}{8}- \dfrac{80}{8}[/tex]
[tex]=\dfrac{-1}{2}x -\dfrac{101}{8}[/tex]
[tex]=\dfrac{-4}{8}x -\dfrac{101}{8}[/tex]
[tex]=\dfrac{-4x-101}{8} [/tex]
[tex]=-\dfrac{4x+101}{8} [/tex]
