Consider the equation. Determine whether the graph of the equation opens upward or downward.

$\begin{gathered} y=(1)/(4)(x-5)^2-3 \\ (x-5)^2=x^2+2(x)(-5)+(-5)^2 \\ (x-5)^2=x^2-10x+25 \\ Hence \\ y=(1)/(4)(x^2-10x+25)^{}-3 \\ y=(1)/(4)x^2-(10x)/(4)+(25)/(4)^{}-3 \\ y=(1)/(4)x^2-(10x)/(4)+(13)/(4)^{} \\ if\text{ a>0, it opens up, in this case a=}(1)/(4),\text{ and }(1)/(4)>0,\text{ therefore the equation opens upward} \\ \\ \text{Questions 2} \\ y=2(x-5)^2-3 \\ y=2(x^2-10x+25)-3 \\ y=2x^2-20x+50-3 \\ y=2x^2-20x+47 \\ (1)/(4)<2,\text{ then} \\ \text{The graph of the equation is wider} \end{gathered}$

Consider the equation. Determine whether the graph of the equation opens upward or-example-1

Consider the equation. Determine whether the graph of the equation opens upward or-example-2

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