# How do you find the vertex and intercepts for #y = x^2 - 4x + 4#?

Vertex:

y-intercept:

x-intercept:

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To find the vertex of the parabola represented by the equation (y = x^2 - 4x + 4), use the formula (x = -\frac{b}{2a}), where (a) is the coefficient of (x^2) (which is 1) and (b) is the coefficient of (x) (which is -4). The x-coordinate of the vertex is (x = -\frac{-4}{2(1)} = 2). To find the y-coordinate, substitute the x-coordinate into the equation: (y = (2)^2 - 4(2) + 4 = 4 - 8 + 4 = 0). So, the vertex is (2, 0). To find the x-intercepts, set (y = 0) and solve for (x): (0 = x^2 - 4x + 4). This equation factors to ((x - 2)^2 = 0), so the only solution is (x = 2). Therefore, the parabola intersects the x-axis at (x = 2). Since the vertex is also at (x = 2), the x-intercept and the vertex coincide.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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