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)

Question

anonymous · Answer

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

anonymous · Answer

solved it, go to you original post

anonymous · Answer

so here you have 4 equations

anonymous · Answer

$$y+1=-(x-4)^2$$ $$y= -x^2+3x-4$$ $$y=(x+1)(x-3)$$ $$y=-(x+1)(x-3)$$

anonymous · Answer

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

anonymous · Answer

yeah hold on

anonymous · Answer

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).

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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 $$y=x^2 + 3$$

anonymous · Answer

thanks guys!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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