# What is x if 2x 2

## Calculate x-value

The **Calculation of the x-value** at a given y-value is more difficult.

Here the y-value or f (x) has to be equated with the given function and the resulting equation has to be solved for x (The different methods for solving equations are discussed in the module "Analysis Basics").

f (x) = $ x ^ 2-6x + $ 9

Exercise: Calculate the x-coordinate for f (x) = 4

1. The 4 is equated with the entire function

4 = $ x ^ 2-6x + $ 9

2. The equation is solved for x. Since it is a quadratic equation, the normal form is made and then solved using the pq formula.

4 = $ x ^ 2-6x + 9 $ / -4

$ 0 = x ^ 2-6x + $ 5

p = -6 q = 5 Find p and q (**Don't forget the sign!**)

$ x_ {1,2} $ = - $ \ frac {-6} {2} \ pm \ sqrt {(\ frac {-6} {2}) ^ 2-5} $

$ x_ {1,2} $ = 3 $ \ pm \ sqrt {9-5} $

$ x_ {1,2} $ = 3 $ \ pm \ sqrt {4} $

$ x_ {1,2} $ = 3 $ \ pm $ 2

$ x_ {1} $ = 5

$ x_ {2} $ = 1

With CAS-TR: use solve function

With GTR-TR: Determine the intersections of $ y_1 = 4 $ and $ y_2 = x ^ 2-6x + 9 $.

y and f (x) is the same, so y = f (x)

The calculation of the zeros (f (x) = 0), the extreme points (f´ (x) = 0) or the turning points (f´´ (x) = 0) are typical tasks in this area. Here the function or the derivatives are equated with 0.

The x-value often has to be calculated in high school exams as well. Since x is often the time, points in time at which something happens must often be calculated. An example is calculated in the following video based on a high school graduation task.

### Video: calculate x-value

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