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PLEASE HELP WITH ALGEBRA AND SHOW WORK :) an explanation would be nice too because this topic confuses me :/

The function f(t) = t^2 + 4t − 14 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for f(t).

Respuesta :

konrad509

A.

[tex] f(t) = t^2 + 4t-14\\
f(t)=t^2+4t+4-18\\
f(t)=(t+2)^2-18
[/tex]


B.

[tex] f(x)=(x-h)^2+k \Rightarrow \text{vertex}=(h,k)\\\\
f(t)=(t+2)^2-18 \Rightarrow \text{vertex}=(-2,-18) [/tex]


It's a minimum, becuase [tex] a=1>0 [/tex].


C.

The axis of symmetry is [tex] x=h [/tex]. So, in this case, it's [tex] x=-2 [/tex].


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