4.2.1 4.2.2 4.2.3 Write down the y-coordinate of C. Determine the coordinates of D. Determine the values of a and q.

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Q: 4. Consider f(x) = -2x² + 3x - 1. a) Find the vertex by completing the square b) Find f-¹(x)

A: I have explained everything with in the solution. Please go through that.

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Q: 6. How many permutations of {0, 1, 2, 3, ..., n,} leave at least two numbers fixed?

A: How many permutations of {0, 1, 2, ...., n} , leaves at least two number fixed ?

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Q: c) A pole of order 4 at zo = 4; -1 with residure 5, and a simple pole at Z₁ = -i with residue. -².

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Q: 11. Simplify completely: 12. 12. Simplify: √√√√√B¹² 2√3+√27

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Q: Find a basis for the subspace V of P4, where V = {p(x) in P4: p(0) = 0, p'(1) = 0, p"(-1) = 0}.

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Q: (c) and Y2(t) 7. The functions Y₁(t) = t and Y₂(t) = tet form a fundamental pair of solutions to the…

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Q: 13. Show that (a) (b) f x²s+¹e-ax² dx = x²se-ax² dx = s! 2as+1; (s — 1/1 ) ! 2a³+1/2

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Q: 1. Simplify: 2x 4x³ ÷ a) x+1* x² −1

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…