50 points for the full answer to this !

a, b, c) see the attachment

d) y = -34.4762(x -2.44268)² +281.613

Using Desmos is pretty straightforward for doing what the problem statement asks. You make a table, then write an equation for y₁ in terms of x₁ using the tilde (~) for the equal sign. Desmos chooses values of the coefficients to make the curve of best fit and lists those for you.

For part (b) of your question, you will have to copy the values into the form of the equation: replace "a" with its value, "b" with its value, "c" with its value.

The vertex point has been highlighted on the curve, so you can read its coordinates on the graph.

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The equation you write relating x₁ and y₁ can be written in vertex form, so you can have Desmos tell you the appropriate numbers directly. (See the second attachment.) As it works out, you don't have to, because the "a" value and the vertex coordinates are all you need to write the equation in vertex form.

the answer

b. they are parallel and will never intersect.