Question

Help!! 15 points. Step by step explanation.

Answer 1

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

Explanation:

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