3.66. For each rule below, make a table of \( x \) -and \( y \) -values and then graph the rule on graph paper. Label each graplı with its equation. \( 3 \) -66 HW eToo (Desmos) Homewotk Help
a. \( y = x ^ { 2 } \)
c. Compare the graphs. What do you notice?
d. For the graph of \( y = x ^ { 2 } \) , estimatr the \( x \) -values corresponding to \( y = 5 \) .
e. For the graph of \( y = - x ^ { 2 } \) , estimate the \( x \) -values corresponding to \( y = - 10 \) .
d.\(\pm \sqrt{5}\)
9. A board game company models the profit on its latest board game using the quadratic relation
\( P = - 2 x ^ { 2 } + 28 x - 90 , \) where \( x \) is the number of games it produces in hundred thousands and \( P \) is the profit in millions of dollars.
a) What are the break-even points for the company?
b) What is the maximum profit that the company can earn?
The graph of \( y = f ( x ) \) is stretched horizontally by a factor of \( 5 \) , and reflected in the \( x \) -axis. What is the equation of the image graph in terms of \( f \) ?
A. \( y = - f ( 5 x ) \) C. \( y = - f ( \frac { 1 } { 5 } x ) \)
B. \( y = - \frac { 1 } { 5 } f ( x ) \) D. \( y = - 5 f ( x )\)
