For what value of B does the function....

Question

For what value of B does the function
f(x)= -3x^2+Bx-4
have only 1 x-intercept? Find all possible values of B and leave your answer in exact form.

Answer 1

For a quadratic to only have one intercept, the vertex must lie on the x axis. Use the formula -b/2a=x to find the x value of the the vertex. Because you don't know "B", simply plug in -b/2a into every x value of the quadratic. Because we want the vertex to lie where y=zero (on the x axis) set the equation with -b/2a plugged in for x equal to zero. You will have another quadratic formula where B is now the only unknown variable. Solve for B.

 

In numbers/variables:

 

x=-b/2a

 

f(-b/2a)=-3(-b/2a)^2+B(-b/2a)-4

 

0=-3(-b/2a)^2+B(-b/2a)-4  (a=-3)

 

Solve that^