15. 1: Notice and Wonder: Two Sets of Equations What do you notice? What do you wonder? $$ \begin{array}{ll}\text { Set 1: } \ \qquad f(x)=x^{2}+4 x \ g(x)=x(x+4) & p(x)=-x^{2}+6 x-5 \ h(x)=(x+2)^{2}-4 & q(x)=(5-x)(x-1)\end{array} $$ $$ r(x)=-1(x-3)^{2}+4 $$

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1. The functions include quadratic and factored forms, some in vertex form. 2. The function $$ r(x) $$ has a vertex at $$ (3, 4) $$ and opens downwards. 3. The functions $$ g(x) $$ and $$ q(x) $$ are factored, making it easy to find their roots. 4. Quadratic functions are symmetric. 5. The equations are in various forms, offering different insights. 6. Questions about intercepts, behavior at infinity, vertex locations, graphing, transformations, and comparative analysis are raised.

15. 1: Notice and Wonder: Two Sets of Equations What do you notice? What do you wonder? \[ \begin{array}{ll}\text { Set 1: } \\ \qquad f(x)=x^{2}+4 x \\ g(x)=x(x+4) & p(x)=-x^{2}+6 x-5 \\ h(x)=(x+2)^{2}-4 & q(x)=(5-x)(x-1)\end{array} \] \[ r(x)=-1(x-3)^{2}+4 \]

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15. 1: Notice and Wonder: Two Sets of Equations What do you notice? What do you wonder? \[ \begin{array}{ll}\text { Set 1: } \\ \qquad f(x)=x^{2}+4 x \\ g(x)=x(x+4) & p(x)=-x^{2}+6 x-5 \\ h(x)=(x+2)^{2}-4 & q(x)=(5-x)(x-1)\end{array} \] \[ r(x)=-1(x-3)^{2}+4 \]

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