I need help in identifying a graph. I tried textbook and plugging no. with no luck
All numbers on right side of (y) line. Bottom of parabola is on x=4 and y=-4, going up f(x) dot is on x=3, y=-3 (left line going up); right line going up is x=5, y= -3; going up again dots on x lt side at x=2, rt side x=6; up again: lt side x=1, y=5; rt side x=7, y=5. Thanks for help.
man! what a lot of words! Why not just list the points on the graph?
(4,-4),(3,-3),(5,-3)
Right there we see the vertex is at (4,-4), so
y = a(x-4)^2 - 4
Now we have points (1,5),(7,5)
5 = a(-3)^2 - 4 = 9a-4
a = 1
so, y = (x-4)^2 - 4
To identify the graph based on the given information, we can start by noting some key characteristics of the graph:
1. The bottom of the parabola is at x = 4 and y = -4.
2. There is a dot on the left side of the graph at x = 3 and y = -3 (going up).
3. There is a dot on the right side of the graph at x = 5 and y = -3 (going up).
4. There are dots on both the left and right sides of the graph at x = 2 and x = 6 (going up).
5. There are dots on both the left and right sides of the graph at x = 1 and x = 7 (going up).
Based on these characteristics, it appears that the graph described is a symmetric parabola with its vertex at (4, -4) and an axis of symmetry at x = 4. The dots on the graph represent points on the parabola.
To visually verify this, you can use various graphing tools such as graphing calculators or online graphing websites. Just enter the equation of a parabola in vertex form and plot the given points to check if they align with the description provided.