source : socratic.org

## For which value of m does the graph of y=18x^2+mx+2 have exactly one x-intercept?

As #y=18x^2+mx+2# will have two intercepts on #x#-axis given by

#18x^2+mx+2=0#

If the discriminant is zero the intercepts will coincide.

As the discriminant is #m^2-4xx2xx18=m^2-144#,

we will have exactly one intercept if #m^2-144=0# or #m=+-12#

i.e. for #y=18x^2-12x+2# and #y=18x^2+12x+2#

graph{18x^2-12x+2 [-3, 3, -2, 5]}

graph{18x^2+12x+2 [-5, 5, -2, 5]}

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