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1), \( (x-5)^{2}-5(x-5)+6 \)

Ask by Flynn Fleming. in South Africa
Jan 21,2025

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\( x^{2}-15x+56 \)

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Bonus Knowledge

Let's simplify the expression step by step. First, substituting \( y = x - 5 \) gives us \( y^2 - 5y + 6 \). This can be factored as \( (y - 2)(y - 3) \). Replacing \( y \) back, we have \( (x - 5 - 2)(x - 5 - 3) = (x - 7)(x - 8) \). Thus, the expression simplifies to \( (x - 7)(x - 8) \). Now, let's talk about how this relates to graphing! The equation \( (x-7)(x-8) = 0 \) reveals that the roots are \( x = 7 \) and \( x = 8 \). These roots are where the parabola hits the x-axis, and it’s helpful for understanding features like vertex and direction of the opening. It's like finding the secret hideouts of a treasure map!

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