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kassia
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)
All right, when you graph the function \[y=x^{2}\] you get a parabola, centered at the origin, it faces up
solved it, go to you original post
so here you have 4 equations
\[y+1=-(x-4)^2\] \[y= -x^2+3x-4\] \[y=(x+1)(x-3)\] \[y=-(x+1)(x-3)\]
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
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).
you want an x intercept of 3, therefore then y=0, the function will x will be 3
Also we know this a downward facing parabola because of the negative sign
so how do you tell which equation will make what type of parabola?
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
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.
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 \[y=x^2 + 3\]
now consider the x intercept of 3, that means when y=0, the function will equal 3.... we now have \[y=x^2+3\]
we want this function to me moved to the right 3 units
sorry, this isn't the right approach, let's just analyze the given functions, however, it seems your question was already answered