It would be easier to just factor since this polynomial is a perfect square, but since your teacher is asking you to use the quadratic formula, we'd better do that too:

You have:

y = ax2 + bx + c

y = x^2 - 3x + 9/4

a = 1, b = -3, c = 9/4

The quadratic formula gives you the values of x when y = 0:

x = (-b + or - square root (b^2-4ac)) / 2a

x = (3 + or - square root (9 - 9)) / 2

x = (3 + sqrt(0) )/ 2 ; (3 - sqrt(0) )/ 2

x = 3/2

You can use factoring or completing the square to check your answer, or graph it on your calculator to double check your answer.

Hope this helps!

Hello Ty, 

you will need both the binomial formula here and the "complete the square" step to transform your equation. The expression on the left happens to be a perfect binomial already and you can transform it to its basic expression being (x-3/2)^2.
Now the only way that this expression is ever zero, is when the value in brackets is zero. Which is only true when x=3/2. Then you'll have (3/2 - 3/2)^2 = 0 or 0^2=0

This is a perfect square.

(x - 3/2)^2 = 0

Answer: x = 3/2