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liberstina [14]
2 years ago
15

Help!! 15 points. Step by step explanation.

Mathematics
1 answer:
Anvisha [2.4K]2 years ago
3 0

Answer:  \bold{f(x)=2\bigg(x+\dfrac{3}{4}\bigg)^2+\dfrac{-25}{8} }

<u>Step-by-step explanation:</u>

f(x) = 2x² + 3x - 2

\text{Add 2 to both sides:}\\f(x) + 2 = 2x^2+3x\\\\\\\text{Factor out 2 on the right side:}\\f(x) + 2 = 2\bigg(x^2+\dfrac{3}{2}x\bigg)\\\\\\\text{Add the value that creates a perfect square on the right side:}\\f(x) + 2 + 2\bigg(\dfrac{3}{2\cdot2}\bigg)^2=2\bigg[x^2+\dfrac{3}{2}x+\bigg(\dfrac{3}{2\cdot2}\bigg)^2\bigg]\\\\\\\text{Simplify:}\\f(x)+2+\dfrac{9}{8}=2\bigg(x+\dfrac{3}{4}\bigg)^2\\\\\\\text{Isolate f(x):}\\f(x)=2\bigg(x+\dfrac{3}{4}\bigg)^2+\dfrac{-25}{8}\\

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