# What is the range of #f(x)=25x^2-30x+16#?

##### 1 Answer

#### Explanation:

The range of a function is the set of all the y-coordinates that are represented in the function. A good way to tell range can be simply through looking at a graph.

graph{25x^2-30x+16 [-15.19, 16.85, -2.13, 15.56]}

This is the graph of

We can determine the range algebraically. The vertex of the parabola is the lowest point of the function, so, if we can determine its y-value, we know where the range begins.

So, to figure out the location of the vertex, we can use the vertex formula for a parabola

First, we figure out the x-coordinate of the vertex by plugging in

Then, to figure out the y-coordinate (this is the one that matters), we find

We get:

Therefore, the coordinate of the vertex is

This means that the function's lowest y-value is