## Question

###### Determine the number of real solutions y= x^2-4x+4? A. 0 B. 1 C. 2 D. 3

Determine the number of real solutions y= x^2-4x+4? A. 0 B. 1 C. 2 D. 3

## Answers

#1# real solution## Explanation:

The key realization is that when we think about how many solutions a quadratic of the form

#ax^2+bx+c# will have, we like to look at the discriminant,

#b^2-4ac# . This is notoriously the quantity under the radical in theQuadratic Formula.We have three cases:

#b^2-4ac>0=>2# real solutins

#b^2-4ac<0=># no real solutions

#b^2-4ac=0=>1# real solutionIn our quadratic, we know

#a=1, b=-4, c=4# , so we can plug these values into our expression for the discriminant:

#16-4(4)=16-16=0# We see that our discriminant is zero, which means this quadratic has one real solution.

Hope this helps!

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