1. Find expressions for the quadratic functions

Find expressions for the quadratic functions whose graphs are shown:

2. Originally Posted by question111
Find expressions for the quadratic functions whose graphs are shown:

there are several ways to approach this. here's one

note that the vertex is on the x-axis, that is, we have a double root for the vertex

thus, our quadratic is of the form $y = a(x - 3)^2$

we are given that the point (4,2) is on the graph, we can use this to find $a$, by plugging in $x = 4$ and $y = 2$ into the form above

3. Originally Posted by question111
Find expressions for the quadratic functions whose graphs are shown:

Your image is so small that it is very hard to see the co-ordinate of vertex and a point in parabola. Please write these coordinates, then it will be solved.

4. Originally Posted by Shyam
Your image is so small that it is very hard to see the co-ordinate of vertex and a point in parabola. Please write these coordinates, then it will be solved.
if you click on the image, it takes you to a larger one

5. So a would be 2, and when I plug that in, I am finally getting a graph like it's shown in the book.

Thank you very much.

6. Originally Posted by question111
So a would be 2, and when I plug that in, I am finally getting a graph like it's shown in the book.

Thank you very much.

7. and so what is your expression

8. Originally Posted by lovegreen
i do not understand your question. we found that a = 2. just plug that into the expression given in post #2 to get the quadratic

9. Thanks!

I see it is y = 2(x squared) -12x + 18

10. Originally Posted by lovegreen
I see it is y = 2(x squared) -12x + 18
Why not just leave it as $y= 2(x- 3)^2$?