# What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola #y=-x^2+2x-5#?

##### 2 Answers

#### Explanation:

All you Need can you see in the following formula

See below:

#### Explanation:

To find the answers in a more straightforward manner, let's first convert from standard form to vertex form. To do that, we're changing from

into

To do that, we complete the square:

**Vertex**

In this form, the vertex (or, in other words, the "pointy bit") is given to us in the

**Axis of Symmetry**

The axis of symmetry splits the parabola in 2 equal parts. It runs through the vertex straight up and down (for a parabola that either opens up or opens down). And so we can write an equation for the line that is vertical and runs through the vertex. In this question, it's

**Maximum/minimum value**

Here we're dealing with looking at the vertex and seeing if it is as high as the parabola goes (i.e. maximum and is when there is a negative sign sitting in front of the

In our case, there's a negative sign and so this will be a maximum. The

**Range**

Since we know the maximum value is

To see all of this in graph form, here's the graph:

graph{-x^2+2x-5[-10,10,-10,0]}

For more on parabolas, you may find this helpful:

http://jwilson.coe.uga.edu/emt725/class/sarfaty/emt669/instructionalunit/parabolas/parabolas.html