91Ó°ÊÓ

Describe a real-life situation that can be modeled by a quadratic equation. Justify your answer.

\(f(x)=(x+6)^2+3\); horizontal shrink by a factor of \(\frac{1}{2}\) and a translation 1 unit down, followed by a reflection in the \(x\)-axis

The table shows the heights y of a competitive water-skier x seconds after jumping off a ramp. Write a function that models the height of the water-skier over time. When is the water-skier 5 feet above the water? How long is the skier in the air? $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Time (seconds), } \boldsymbol{x} & 0 & 0.25 & 0.75 & 1 & 1.1 \\\ \hline \text { Height (feet), } \boldsymbol{y} & 22 & 22.5 & 17.5 & 12 & 9.24 \\\ \hline \end{array} $$

The path of a basketball thrown at an angle of \(45^{\circ} \mathrm{can}\) be modeled by \(y=-0.02 x^2+x+6\).

The path of a shot put released at an angle of \(35^{\circ} \mathrm{can}\) be modeled by \(y=-0.01 x^2+0.7 x+6\).

The table shows the number of tiles in each fi gure. Verify that the data show a quadratic relationship. Predict the number of tiles in the 12th figure. cant copy graph $$ \begin{array}{|l|c|c|c|c|} \hline \text { Figure } & 1 & 2 & 3 & 4 \\ \hline \text { Number of Tiles } & 1 & 5 & 11 & 19 \\ \hline \end{array} $$

USING STRUCTURE Which function represe the parabola with the widest graph? Explain your reasoning. (A) \(y=2(x+3)^2\) (B) \(y=x^2-5\) (C) \(y=0.5(x-1)^2+1\) (D) \(y=-x^2+6\)

\(g(x)=2(x-1)^2+2\)

Identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with vertex \((\mathbf{0}, \mathbf{0})\). $$y=\frac{1}{8}(x-3)^2+2$$

translation 6 units down followed by a reflection in the \(x\)-axis $$ \begin{aligned} h(x) &=f(x)-6 \\ &=2 x^2+6 x-6 \\ g(x) &=-h(x) \\ &=-\left(2 x^2+6 x-6\right) \\ &=-2 x^2-6 x+6 \end{aligned} $$