## anonymous one year ago Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point. Maximum at (2, –2) Minimum at (2, –2) Maximum at (2, 6) Minimum at (2, 6)

1. Mehek14

since the first term is positive = $$2x^2$$ that means it is opening upwards so the vertex would be the minimum that eliminates A and C

2. Mehek14

to find the vertex, use $$\dfrac{-b}{2a}$$ in your equation, you have b = -8 a = 2 $$\dfrac{-(-8)}{2*2}=\dfrac{8}{4}=2$$ so x = 2

3. Mehek14

plug x = 2 into the equation

4. Mehek14

@boots_2000 can you do that?

5. anonymous

Yeah so is it maximum 2,6?

6. anonymous

@Mehek14

7. IrishBoy123

it says "Using the completing-the-square method"

8. Mehek14

no did you plug in x = 2 in the equation

9. anonymous

yeah

10. welshfella

using completing the square:- = 2(x^2 - 4x + 3) = 2[(x - 2)^2 - c + 3] can you tell me the value of c - can you remember from the last post?

11. Mehek14

$$f(2)=2*2^2-8*2+6\\2^2=4\\2*4=8\\8*2=16\\8-16=-8$$ add $$-8+6$$

12. IrishBoy123

+1 @welshfella

13. anonymous

so its minimum? lol

14. Mehek14

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @Mehek14 since the first term is positive = $$2x^2$$ that means it is opening upwards so the vertex would be the minimum that eliminates A and C $$\color{#0cbb34}{\text{End of Quote}}$$

15. welshfella

its a minimum but what are the coordinates at the minimum?

16. anonymous

2,6

17. Mehek14

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @Mehek14 $$f(2)=2*2^2-8*2+6\\2^2=4\\2*4=8\\8*2=16\\8-16=-8$$ add $$-8+6$$ $$\color{#0cbb34}{\text{End of Quote}}$$

18. welshfella

No mehek has worked the y coordinate for you you can also get from the completing the square method

19. anonymous

so 2,-2

20. Mehek14

yes

21. anonymous

could you guys come and help me quick when you're all done here?

22. welshfella

I'll carry from where i left off 2[(x - 2)^2 - c + 3] c = 4 because -2^2 = + 4 = 2(x - 2)^2 - 1) = 2(x - 2)^2 - 2 so the vertex is at ( 2,-2) you get this by comparing your expression with the genarl form for the vertex

23. anonymous