Use the equation y = ax^2 + bx + c where x is the horizontal distance a baseball has traveled and y is the height of the ball at the given distance.
1)Are some values of y unreasonable?
2)How is this information important for choosing a window for the graph?
3) With respect to the quadratic polynomial, the value of x has a name. what is it called?
I assume some values of y would be unreasonable because you couldn't hit the ball that high. Am I on the right track?
On the graph the distance when the ball landed would be the x-intercept, but I do not know what the value of x is called with respect to the quadratic polynomial. Would it be a root? Please help.
1) Yes, some values of y could be unreasonable depending on the context. Since y represents the height of the ball, negative y-values would not make sense because height cannot be negative in this context. Additionally, extremely large positive values of y would be unreasonable because it is highly unlikely for a baseball to reach such heights.
2) Understanding whether the values of y are reasonable is important for choosing a window for the graph. The window represents the range of values on the x-axis and y-axis that will be displayed in the graph. By considering the reasonable values of y, you can choose an appropriate window that includes all relevant data points without distorting the visualization. For example, if the highest reasonable value of y is 100 feet, then you wouldn't want to choose a window that includes heights that go beyond 100 feet on the y-axis.
3) The value of x in the quadratic polynomial equation y = ax^2 + bx + c does have a name. It is called the independent variable or the input variable. In this context, x represents the horizontal distance, which is the input for the equation that determines the height of the ball (y) at that particular distance. The term "root" is commonly used to refer to the values of x where the quadratic equation equals zero (i.e., the x-intercepts or solutions of the equation), but it is not specifically related to the value of x itself in the context of the quadratic polynomial equation.