algebra correct?

Question

Ok here is the question and my work tell me I did it correctly. If not please show me a correct example.

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.


When the discriminate is positive the graph y=ax^2+bx+c will have two two x-intercepts
Example:

Y= 6x^2+5x+4



{2} When the discriminate is zero the graph of (y+ax2+bx+c) will have one x-intercept.
Example:
Y= 5x^2+5x+1

{3}When the discriminate is negative the graph of (y=ax^2+bx+c) will have no x-intercepts.


Example: Y= 4X2 + 7x + 6

Answer 1

Your equations do not work. The explanation is ok.

b^2-4ac>0 You have 6x^2 +5x + 4 where it would be 25-4(5)4 = 25 - 80 = -55. Change the sign in front of the +4 to negative and it will work.

For the second equation, b^2-4ac must = 0.
You need something where both factors are the same as y = x^2 - 6x + 9 where b^2 - 4ac = 36-4(1)(9) = 0.

The last case is ok.