# Thread: Reasoning and graph problem

1. ## Reasoning and graph problem

The price of a certain item was $10 in 1990 and it has gone up by$2 per year since 1990. If this trend continues, in what year will the price be $100? On average the price increased$2, so $\frac{100 - 10}{2} = 45$
Hence 45 + 1990 = 2035

Graph
The figure above shows the graph of a quadratic function in the xy-plane. Of all the points (x, y) on the graph, for what value of x is the value of y greatest?

Somewhere between 3 and 7? Does it have to be a particular point between 3 and 7?
Perhaps I'm plain wrong?!

2. Originally Posted by Hellbent
The price of a certain item was $10 in 1990 and it has gone up by$2 per year since 1990. If this trend continues, in what year will the price be $100? On average the price increased$2, so $\frac{100 - 10}{2} = 45$
Hence 45 + 1990 = 2035

Graph
The figure above shows the graph of a quadratic function in the xy-plane. Of all the points (x, y) on the graph, for what value of x is the value of y greatest?

Somewhere between 3 and 7? Does it have to be a particular point between 3 and 7?
Perhaps I'm plain wrong?!
1. The graph of a quadratic function is symmetric. The vertex (that's the maximum or minimum point of the graph) is located on the axis of symmetry.

2. Therefore the axis of symmetry bisects the distance between the zeros which will yield the x-coordinate of the maximum point.
The x-coordinate is the mean of the 2 zeros. With your example x = 5.

### the figure above shoes the graph of a quadratic function in the xy plane of the point(x,y)on the graph for what value of x is the value of y greatest

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