Thread: Finding the points to point on a parabola

Hi, I'm having trouble finding some co-ordinates to plot on a parabola. Please list the vertex and x & y axis intercepts.

1) y = 2x^2 - 5x - 7
2) y = -x^2 + 2x + 3
3) y = x^2 - 4x
4) y = (1 - 2x)(x - 5)
5) y = 1/3x^2 + 2x - 4

Thanks.

Hello,

Originally Posted by BG5965

Hi, I'm having trouble finding some co-ordinates to plot on a parabola. Please list the vertex and x & y axis intercepts.

1) y = 2x^2 - 5x - 7
2) y = -x^2 + 2x + 3
3) y = x^2 - 4x
4) y = (1 - 2x)(x - 5)
5) y = 1/3x^2 + 2x - 4

Thanks.

All problems are almost similar.

For 1),2),3),5), complete the square. (A link has been given in your previous thread)

x axis intercepts are points where . So after completing the ssquare, it should be easy !

y axis intercepts are points where , so just substitute x by 0.

Vertex is the point where there is a minimum or maximum. In general and at your level, it corresponds to the point which annulates the square you should have obtained when completing the square.



For 4), first find the x axis intercepts. You find them by saying :
(1-2x)(x-5)=0 iff 1-2x=0 or x-5=0.

Do the same as above for finding the y axis intercepts : substitute x by 0.

For the vertex, you can just develop the product and complete the square.