# How do you solve using the quadratic formula for #y = x^2 - 4x + 4#?

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To solve the equation ( y = x^2 - 4x + 4 ) using the quadratic formula, we first need to identify the coefficients ( a ), ( b ), and ( c ) in the general quadratic equation ( ax^2 + bx + c = 0 ). In this case:

( a = 1 ) ( b = -4 ) ( c = 4 )

Next, we plug these values into the quadratic formula:

[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} ]

Substitute the values:

[ x = \frac{{-(-4) \pm \sqrt{{(-4)^2 - 4(1)(4)}}}}{2(1)} ]

Simplify:

[ x = \frac{{4 \pm \sqrt{{16 - 16}}}}{2} ]

[ x = \frac{{4 \pm \sqrt{0}}}{2} ]

Since the discriminant ( b^2 - 4ac ) is zero, we have a repeated root. Therefore, the solutions are:

[ x = \frac{4}{2} = 2 ] (repeated root)

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