SOLUTION: Please help. i don't know how to do this. I have to write the following in vertex form and tell if they open up or down. 1.The vertex of the parabola is the origin. Point P (

Question 522220: Please help. i don't know how to do this.
I have to write the following in vertex form and tell if they open up or down.
1.The vertex of the parabola is the origin. Point P (1,7) lies on the graph of the parabola.
2.The vertex of the parabola is the origin. Point W (4,-5) lies on the graph of the parabola.
Thanks so much
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
I have to write the following in vertex form and tell if they open up or down.
1.The vertex of the parabola is the origin. Point P (1,7) lies on the graph of the parabola.
2.The vertex of the parabola is the origin. Point W (4,-5) lies on the graph of the parabola.
Thanks so much
**
The best way to do this is plot the two given points, vertex(0,0), and given point P(1,7) on the graph. Since the y-value of the point>0, the parabola must open upwards.
Similarly, for point W(4,-5), the y-value<0, so the parabola must open downwards.
..
To do it algebraically:
Standard form of a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
Since the(x,y) coordinates of both parabolas, boil down to y=Ax^2.
The problem is to find A for the equations of both parabolas.
For the first problem, using (x,y) coordinates of given point (1,7)
7=A(1^2)
A=7
Equation of parabola: y=7x^2
..
For the second problem, using (x,y) coordinates of given point (4,-5)
-5=A(4^2)=16A
A=-5/16
Equation of parabola: -5x^2/16
Plot these two equations and the first will open up and the second opens down.
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