# How do you find the maximum, minimum and inflection points and concavity for the function #f(x) = 2x^2 + 6x + 5#?

##### 2 Answers

This is a quadratic function.

#### Explanation:

A function

It opens upward and is concave up if

The function has a minimum if

The minimum or maximum occurs at the vertex which is at

(If you forget the veertex formula, use the derivative

See below.

#### Explanation:

This is just a standard quadratic. You do not need calculus to solve this problem. The coefficient of

So the function is convex ( concave up ) for

There are no inflection points, because the function is convex for the entire domain. Infection points only occur when the concavity changes.

Maximum value is

( this can be deduced by the fact that the function is concave up for entire domain )

To find the minimum value, we need to arrange the function in form:

Where **a** is the coefficient of **h** is the axis of symmetry and **k** is the maximum/minimum value of the function.

Bracket of the terms containing the variable:

Factor out the coefficient of

Add the square of half the coefficient of

Convert to the square of a binomial:

So minimum value

graph{y=2x^2+6x+5 [-5, 2, -5, 7]}