SOLUTION: for what value(s) of k will the graph of y = x^2-3x+k a) touch the x-axis b) never meet the x-axis?

Question 155245: for what value(s) of k will the graph of y = x^2-3x+k
a) touch the x-axis
b) never meet the x-axis?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

It will touch the x-axis when the polynomial has only one solution. If the polynomial has only one solution, then the discriminant is equal to zero.

Start with the discriminant formula

Plug in , , and

Square -3 to get 9

Multiply

Subtract 9 from both sides

Divide both sides by -4

So when , then the polynomial will have only one solution and will touch the x-axis.

b)

Follow the same procedure described above, but this time .
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