without graphing deteermine the number of x intercepts of the graph of y=4x^2-9x+4
for waht values of b does the quadratic function y=x^2+bx+7 have no x intercepts?
for what values does the quadratic function y=x^2-6x+k have two x intercepts?
for what value of k does the quardatic function y=-3x^2-bx+12 have exatcly one x intercept?
You can tell a lot about a quadratic by looking at its discriminant
If the discriminant is positive, then it has two real and unequal roots.
If it is 0, then it has one root of mutiplicity 2.
If it is negative, then it has no real roots.
For the second one,
If it does not cross the x-axis, then it has no real roots and the discrimiant must be negative.
See?. Try it with the other problems.