## anonymous one year ago without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y=2x^2+x-3 A. 2 points in common; vertex below x-axis B. no points in common; vertex below x-axis C. 1 point in common; vertex on x-axis D. 2 points in common; vertex above x-axis

1. anonymous

Do you know how to tell whether the graph opens up or down?

2. anonymous

if the coefficient of x² is positive the parabola opens up. If it's negative the parabola opens down

3. anonymous

and to find the x-coordinate of the vertex use x = -b/(2a)

4. anonymous

so, the coefficient of x^2 is 2, right?

5. anonymous

right

6. anonymous

so which way does the parabola open?

7. anonymous

up

8. anonymous

ok. so now let's find the vertex. For a quadratic equation ax²+bx+c, the x-coordinate of the vertex is $x=\frac{ -b }{ 2a }$

9. anonymous

i got -1/4=-0.25

10. anonymous

right. Now plug -1/4 in for x in your original formula to find the y-coordinate.

11. anonymous

i got -4.25? which answer is that?

12. anonymous

I got -3.125

13. anonymous

show me what you did, please

14. anonymous

|dw:1433124251446:dw|

15. anonymous

okay, so which answer is that? is the vertex below the x-axis?

16. anonymous

right, below the x-axis

17. anonymous

and if it open up, in how many places does it cross the x-axis?

18. anonymous

i... i dunno.

19. anonymous

i'm guessing two?

20. anonymous

yes|dw:1433124522429:dw|

21. anonymous

can you help me with one more? that'll be all I need help with. and thanks for helping me.

22. anonymous

ok