Graphing radical functions: h(t)=-4.9(t+3)^2+45.8 was asked to find inverse.

[Don't Drink and Derive]

Hello, I'm working with quadratic function h(t)=-4.9(t+3)^2+45.8 was asked to find inverse. Obtained h-1(t)=sqrrt[((t-45.8)/-4.9)]-3(side question: Is there a way to simplify this inverse)
Main question how do I graph radical functions. Is making a table of t/h-1(t) values the only way to graph radicals? Or is there a formula e.x. (vertex form, factored form) for radical functions?

Thank you for your assistance!

 

[stapel]

I'm working with quadratic function h(t)=-4.9(t+3)^2+45.8. I was asked to find inverse. I obtained:

. . .h^-1(t) = sqrt[((t-45.8)/-4.9)] - 3

(side question: Is there a way to simplify this inverse?)

Well, you can get rid of a "minus" sign by flipping the subtraction:

. . . . .\(\displaystyle h^{-1}\, =\, \sqrt{\strut \dfrac{45.8\, -\, t}{4.9}\,}\, -\, 3\)

But anything past much past that would probably be a waste of time.

My main question is, "How do I graph radical functions?" Is making a table of t/h-1(t) values the only way to graph radicals? Or is there a formula e.x. (vertex form, factored form) for radical functions?

A T-chart is probably the simplest way to go. Just plot points, the same as you've always done.

 

[lookagain]

Hello, I'm working with quadratic function h(t)=-4.9(t+3)^2+45.8 was asked to find inverse. Obtained h-1(t)=sqrrt[((t-45.8)/-4.9)]-3

That's not a one-to-one function. $\displaystyle \ \ h(t) \ = \ -4.9(t + 3)^2 \ + \ 45.8, \ \ t \ \ge -3 \ \$ is a one-to-one function associated with that quadratic function.


Its inverse is $\displaystyle \ \ h^{-1}(t) \ = \ \sqrt{ \dfrac{45.8 - t}{4.9}} \ - \ 3, \ \$ as was mentioned above.

 

[stapel]

That's not a one-to-one function...

So the poster cannot find the inverse function (since there isn't one), but the poster can find "the inverse" (being just a relation).