# [SOLVED]IB23. A family of functions is given by...calculate the probability

#### karush

##### Well-known member
View attachment 1183

well by completing the square from $x^2+3x$ we get $\pmatrix {x+\frac{3}{2}}^2 -\frac{9}{4}$
which means the vertex is more than $2$ below the x-axis but above at $3$

so from the set k only at $k=1$ and $k=2$ will it cross the x-axis so $\frac{2}{7}$ is the probability that the function will cross the x-axis.

one way i guess

#### agentmulder

##### Active member
You could also use the discriminant of f(x).

$3^2 - 4k > 0$

Works only for k = 1 . k = 2