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\( \left. \begin{array} { l } { h ( x + a ) = ( x + a ) ^ { 2 } - 4 ( a + 8 ) - 6 } \\ { x \rightarrow x + c = x ^ { 2 } + a ^ { 2 } - 4 a - 32 - 6 } \end{array} \right. \)

Ask by Schofield Nguyen. in the United States
Mar 11,2025

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\( a = 0 \) and \( c = 0 \).

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The Deep Dive

Did you know that completing the square is a powerful technique in algebra that can help you rearrange quadratic equations for easier understanding and solution? This method not only aids in solving equations but also in graphing them. In your function, by manipulating \( h(x + a) \), you can represent the vertex form of a parabola, giving insight into its maximum or minimum value based on the coefficient of the squared term. In real-world situations, quadratic functions like the one you've provided can model various phenomena, such as projectile motion or profit maximization in a business scenario. Consider an object being thrown; its height as a function of time can be represented by a quadratic equation, allowing you to predict when it will reach its peak height and when it will hit the ground. It's not just math; it's everywhere!

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