help please! and let me know how you got to that answer

[reginajohn]

Find the value(s) of k so that the graph of
f(x) = kx^2 - 9x + 6 has:
a) two x-intercepts
b) one x-intercept
c) no x-intercept

 

[Dr.Peterson]

Find the value(s) of k so that the graph of
f(x) = kx^2 - 9x + 6 has:
a) two x-intercepts
b) one x-intercept
c) no x-intercept

I would find the discriminant (as a function of k), and determine for what values of k it is positive, negative, and zero.

 

[HallsofIvy]

Do you understand what "x-intercept" means?? An an "x-intercept" is a point on the graph where y= 0. In other words you want to find x such that \(\displaystyle kx^2- 9k+ 6= 0\).

By the quadratic formula, \(\displaystyle x= \frac{9\pm\sqrt{81- 24k}}{2k}\).

If the quantity inside the square root (the "discriminant" Dr. Peterson referred to) is positive then you have two real number roots, one for the "+" and one for the "-". If it is 0, there is just one and if it is negative there are none.