The domain of the graph is the set of all real values
<h3>How to determine the domain?</h3>
The domain is the set of x values of the graph
From the graph, the x values extend in both directions without end
This means that the x values can accommodate all real values
Hence, the domain of the graph is the set of all real values
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Answer: 
<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}\\](https://tex.z-dn.net/?f=%5Ctext%7BAdd%202%20to%20both%20sides%3A%7D%5C%5Cf%28x%29%20%2B%202%20%3D%202x%5E2%2B3x%5C%5C%5C%5C%5C%5C%5Ctext%7BFactor%20out%202%20on%20the%20right%20side%3A%7D%5C%5Cf%28x%29%20%2B%202%20%3D%202%5Cbigg%28x%5E2%2B%5Cdfrac%7B3%7D%7B2%7Dx%5Cbigg%29%5C%5C%5C%5C%5C%5C%5Ctext%7BAdd%20the%20value%20that%20creates%20a%20perfect%20square%20on%20the%20right%20side%3A%7D%5C%5Cf%28x%29%20%2B%202%20%2B%202%5Cbigg%28%5Cdfrac%7B3%7D%7B2%5Ccdot2%7D%5Cbigg%29%5E2%3D2%5Cbigg%5Bx%5E2%2B%5Cdfrac%7B3%7D%7B2%7Dx%2B%5Cbigg%28%5Cdfrac%7B3%7D%7B2%5Ccdot2%7D%5Cbigg%29%5E2%5Cbigg%5D%5C%5C%5C%5C%5C%5C%5Ctext%7BSimplify%3A%7D%5C%5Cf%28x%29%2B2%2B%5Cdfrac%7B9%7D%7B8%7D%3D2%5Cbigg%28x%2B%5Cdfrac%7B3%7D%7B4%7D%5Cbigg%29%5E2%5C%5C%5C%5C%5C%5C%5Ctext%7BIsolate%20f%28x%29%3A%7D%5C%5Cf%28x%29%3D2%5Cbigg%28x%2B%5Cdfrac%7B3%7D%7B4%7D%5Cbigg%29%5E2%2B%5Cdfrac%7B-25%7D%7B8%7D%5C%5C)
Latus rectum is the line segment that passes through the focus, is perpendicular to the axis, and has both endpoints on the curve.
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