help_people one year ago The function f(t) = t2 + 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).

1. help_people

i have all the parts ecvept for a

2. Astrophysics

So you want to complete the square?

3. Astrophysics

If you have $x^2+ax=0$ we can do the following $x^2+\frac{ 2ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2=0$ (complete the square)

4. Astrophysics

But don't forget about third term, you just add that, so I'll show what I mean by starting it off |dw:1443909088007:dw| now you can factor

5. Astrophysics

|dw:1443909240041:dw|

6. help_people

so whats the ansswer and what do you want me to factor?

7. Astrophysics

$(t^2+4t+4)-14-4=0$ factor $(t^2+4t+4)$

8. help_people

(t+2)^2 (factor)

9. Astrophysics

Right so you have $(t+2)^2-18$

10. Jhannybean

$(t^2+4t)-14\qquad \qquad c=\left(\frac{4}{2}\right)^2 = (\color{red}{2})^2=4$$(t^2+4t+4)-14-4$$=(t+\color{red}{2})^2-18$

11. Astrophysics

The process above is what is called completing the square, we often use it if we are unable to factor what we have, to check if something if factorable we check the discriminant $b^2-4ac<0$ see if it's less then 0 it means we cannot factor and have to use complete the square or another method such as quadratic formula.

12. Jhannybean

The formula for completing the square: $$\left(x\pm \dfrac{b}{2}\right)^2 \pm b^2\pm c$$

13. Jhannybean

I believe that's it...

14. help_people

THANKS EVERYBODY: )))))