What is the x-intercept of the graph of y =x2-4x+4

1 answer:

4 0

  y = x² - 4x + 4
  0 = x² - 4x + 4
  0 = x² - 2x - 2x + 4
  0 = x(x) - x(2) - 2(x) - 2(-2)
  0 = x(x - 2) - 2(x - 2)
  0 = (x - 2)(x - 2)
  0 = (x - 2)²
  0 = x - 2
+ 2 + 2
  2 = x
(x, y) = (2, 0)

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Answer with explanation:

The coordinates of four points of Quadrilateral ABCD are

A(4, 5), B(–7, –10), C(–4, –9), D(7, 6)

$AB=\sqrt{(4+7)^2+(5+10)^2}\\\\AB=\sqrt{121+225}\\\\AB=\sqrt{346}\\\\BC=\sqrt{(-7+4)^2+(-10+9)^2}\\\\BC=\sqrt{9+1}\\\\BC=\sqrt{10}\\\\CD=\sqrt{(4+7)^2+(5+10)^2}\\\\CD=\sqrt{121+225}\\\\CD=\sqrt{346}\\\\DA=\sqrt{(7-4)^2+(6-5)^2}\\\\DA=\sqrt{9+1}\\\\DA=\sqrt{10}$

Slope between two points is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m_{1}=\frac{-10-5}{-7-4}\\\\=\frac{-15}{-11}\\\\m_{1}=\frac{15}{11}\\\\m_{2}=\frac{-9+10}{-4+7}\\\\m_{2}=\frac{1}{3}\\\\m_{3}=\frac{6+9}{7+4}\\\\m_{3}=\frac{15}{11}\\\\m_{4}=\frac{6-5}{7-4}\\\\m_{4}=\frac{1}{3}$