kassia 4 years ago Which one of these equations would make a graph with a downward facing parabola with an x intercept of 3 and a y intercept of 3 y+1=-(x-4)^2; y= -x^2+3x-4; y=(x+1)(x-3); y=-(x+1)(x-3)

1. AntiMatter

All right, when you graph the function \[y=x^{2}\] you get a parabola, centered at the origin, it faces up

2. LagrangeSon678

solved it, go to you original post

3. AntiMatter

so here you have 4 equations

4. AntiMatter

\[y+1=-(x-4)^2\] \[y= -x^2+3x-4\] \[y=(x+1)(x-3)\] \[y=-(x+1)(x-3)\]

5. kassia

i saw that you solved it for a second and then the computer im on decided to be uncoperative so i can no longer view it is it possible for you to copy and paste sorry for the hassle

6. LagrangeSon678

yeah hold on

7. LagrangeSon678

The answer to your question is : y=-(x+1)(x-3). Why? becuase from the factored form we see that there will be an xintercept at (3,0). TO get the y intercept you have to replace x with zero and evluate. you will get (0,3).

8. AntiMatter

you want an x intercept of 3, therefore then y=0, the function will x will be 3

9. LagrangeSon678

Also we know this a downward facing parabola because of the negative sign

10. kassia

so how do you tell which equation will make what type of parabola?

11. LagrangeSon678

Will a downward facing parabola should have a negative sign on the leading term. It is best to expand y=-(x+1)(x-3), You should get y=-x^2-2x-3

12. LagrangeSon678

now that you have this expaned, you can see that this indeed will be a parabola because of the x^2 term. Then you also have the factored form. To get the x and y intecepts, in this case, it is good to use the factored from. To get y-int set x to be zero and solve. To get x-intercpet set y to be zero and solve.

13. AntiMatter

so starting with \[y=x^2\] we can transform this into the equation we want. so y intercept of 3, that means when x = 0 the function will equal 3, therefore, consider the basic parabola, \[3=(0^2)\], so you need to add 3 therefore it becomes \[y=x^2 + 3\]

14. kassia

thanks guys!

15. AntiMatter

now consider the x intercept of 3, that means when y=0, the function will equal 3.... we now have \[y=x^2+3\]

16. AntiMatter

we want this function to me moved to the right 3 units

17. AntiMatter

sorry, this isn't the right approach, let's just analyze the given functions, however, it seems your question was already answered