# 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 \$.