# How do you determine the range of a quadratic function?

##### 1 Answer

#### Answer:

See below

#### Explanation:

Assuming you mean a polynomial of degree

they will always represent a parabola. Depending on the sign of

**Case 1: #a>0#**

In this case, the parabola "points upwards" This means that the vertex of the parabola is its global minimum, and so the graph can't reach any point lower than the vertex. On the other hand, the parabola stretches towards infinity as

Here's an example: the vertex is the point

graph{x^2+3x-1 [-7 7 -4 9]}

**Case 2: #a>0#**

This case is the opposite of the previous one. In this case, in fact, the vertex is the global maximum of the parabola, and there is no lower bound. Everything else remains the same: the range is thus given by

If you consider the example

graph{-3x^2 + 15x - 4 [-1 6 -5 19]}