Hello Feep! Since you are trying to to find the minimum value, you can use the vertex formula.
a = 1
b = -14
Vertex Formula.
[tex]x = -\frac{b}{2a}[/tex]
[tex]x = -\frac{(-14)}{2(1)}[/tex]
Distrubute the negative to the -14 making it 14
[tex]x = \frac{(14)}{2(1)}[/tex]
Times the denominator 2 * 1 = 2
[tex]x = \frac{(14)}{2}[/tex]
[tex]x = 7[/tex]
So 7 will give the minimum value for x^2- 14x + 3