91Ó°ÊÓ

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

The graph is a reflection in the \(y\)-axis and a vertical stretch by a factor of 6 , followed by a translation 4 units up of the graph of the parent quadratic function.

The table shows the distances y a motorcyclist is from home after x hours. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Time (hours), } \boldsymbol{x} & 0 & 1 & 2 & 3 \\ \hline \text { Distance (miles), } \boldsymbol{y} & 0 & 45 & 90 & 135 \\ \hline \end{array} $$

The table shows the heights h (in feet) of a sponge t seconds after it was dropped by a window cleaner on top of a skyscraper. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Time, } \boldsymbol{t} & 0 & 1 & 1.5 & 2.5 & 3 \\ \hline \text { Height, } \boldsymbol{h} & 280 & 264 & 244 & 180 & 136 \\ \hline \end{array} $$ a. Use a graphing calculator to create a scatter plot. Which better represents the data, a line or a parabola? Explain. b. Use the regression feature of your calculator to find the model that best fits the data. c. Use the model in part (b) to predict when the sponge will hit the ground. d. Identify and interpret the domain and range in this situation.

Your friend states that quadratic functions with the same x-intercepts have the same equations, vertex, and axis of symmetry. Is your friend correct? Explain your reasoning.

WRITING Two quadratic functions have graphs with vertices (2, 4) and (2, ?3). Explain why you can not use the axes of symmetry to distinguish between the two functions.

analyze the differences in the outputs to determine whether the data are linear, quadratic, or neither. Explain. If linear or quadratic, write an equation that fi ts the data. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Time (hours), } \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 \\ \hline \begin{array}{l} \text { Population } \\ \text { (hundreds), } \boldsymbol{y} \end{array} & 2 & 4 & 8 & 16 & 32 \\ \hline \end{array} $$

\(f(x)=x^2\); vertical stretch by a factor of 4 and a reflection in the \(x\)-axis, followed by a translation 2 units up

WRITING A quadratic function is increasing to the left of x = 2 and decreasing to the right of x = 2. Will the vertex be the highest or lowest point on the graph of the parabola? Explain.

\(f(x)=8 x^2-6\); horizontal stretch by a factor of 2 and a translation 2 units up, followed by a reflection in the \(y\)-axis