## egracer one year ago The equation f(x) = 5x2 − 30x + 6 represents a parabola. What is the vertex of the parabola? (−5, 281) (5, −19) (−3, 141) (3, −39)

1. anonymous

In the general equation of a parabola$f \left( x \right) = ax ^{2} + bx + c$The x-coordinate of the vertex is given by$x=-\frac{ b }{ 2a }$Then calculate f(x) using this value of x to give you the y-coordinate of the vertex.

2. egracer

Would it be B?

3. anonymous

Don't think so.

4. egracer

Sorry trying to figure this out haha math isn't my best subject so its a little harder let me try to recalculate

5. anonymous

No problem. Take your time. What do you get for the x-coordinate? (-b/2a)

6. egracer

would the x coordinate be -39/2a?

7. anonymous

Not quite. From looking at the given quadratic, what is the value of a and the value of b?

8. anonymous

a multiplies x^2 and b multiplies the x

9. egracer

honestly I have no clue I'm so confused on how to do this could you explain like in details like how to solve it

10. anonymous

I just did. But let's back up. The given quadratic function is$f \left( x \right) = 5x ^{2} - 30x + 6$Compare that with$f \left( x \right) = ax ^{2} + bx + c$a is the number that multiplies x^2 b is the number that multiplies x What are they?

11. egracer

a is 5 and b is -30??

12. anonymous

Perfect. Now the x-coordinate is given by$x = -\frac{ b }{ a }$Plug in those values of a and b . What do you get?

13. anonymous

Sorry. It's$x=-\frac{ b }{ 2a }$

14. anonymous

So you're calculating$x=-\frac{ b }{ 2a } = -\frac{ -30 }{ 2\left( 5 \right) } = ?$

15. egracer

-75?

16. anonymous

Nope. What is 2 x 5 ?

17. egracer

10

18. anonymous

Good. That's the denominator. Now, what's -30/10 ?

19. egracer

-3

20. anonymous

Good. Finally, what's -(-3) ?

21. egracer

3

22. anonymous

Excellent. So the x-coordinate of the vertex is 3.

23. anonymous

Now, to get the y-coordinate of the vertex, put his value of x into the original function and calculate f(3)$f \left( x \right)=5x ^{2}-30x+6$$f \left( 3 \right) = 5\left( 3 \right)^{2}-30\left( 3 \right) + 6$What do you get?

24. egracer

-18?

25. anonymous

Nope. What is 3^2 ?

26. egracer

9

27. anonymous

Great. Now what is 5 x 3^2 ?

28. egracer

45

29. anonymous

Good. Now what is 30 x 3 ?

30. egracer

90

31. anonymous

Great. Now to put it all together$f \left( 3 \right) = 5\left( 3 \right)^{2} - 30\left( 3 \right) + 6 = 45-90+6 = ?$

32. egracer

-39

33. anonymous

Good. Now you have the x- and y-coordinates of the vertex. Where is the vertex?

34. egracer

35. anonymous

That's it. Well done.

36. egracer

thank you so much for being patient with me! and helping me understand!

37. anonymous

You're welcome. Good luck with your studies.