# How do you find the vertex of the parabola #y = x^2 – 2x + 4#?

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To find the vertex of the parabola y = x^2 - 2x + 4, you can use the formula x = -b / (2a) where "a" is the coefficient of the x^2 term and "b" is the coefficient of the x term in the equation. In this case, a = 1 and b = -2. Plugging these values into the formula, we get x = -(-2) / (2*1) = 1. Therefore, the x-coordinate of the vertex is 1. To find the corresponding y-coordinate, substitute x = 1 into the equation y = x^2 - 2x + 4. So, y = (1)^2 - 2(1) + 4 = 1 - 2 + 4 = 3. Hence, the vertex of the parabola is (1, 3).

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To find the vertex of the parabola represented by the equation ( y = x^2 - 2x + 4 ), we use the formula:

[ x_{\text{vertex}} = -\frac{b}{2a} ] [ y_{\text{vertex}} = f(x_{\text{vertex}}) ]

Where ( a ), ( b ), and ( c ) are the coefficients of the quadratic equation in standard form ( ax^2 + bx + c ).

In the given equation ( y = x^2 - 2x + 4 ): [ a = 1 ] [ b = -2 ] [ c = 4 ]

Substituting these values into the formula, we get: [ x_{\text{vertex}} = -\frac{-2}{2(1)} = 1 ]

Now, we find the corresponding value of ( y ) by substituting ( x = 1 ) into the equation: [ y_{\text{vertex}} = (1)^2 - 2(1) + 4 = 1 - 2 + 4 = 3 ]

Therefore, the vertex of the parabola represented by the equation ( y = x^2 - 2x + 4 ) is ( (1, 3) ).

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