1.How is the maximum or minimum point of the original quadratic function related to the maximum or minimum point of its reciprocal function?

2.How can you use the leading coefficient of the original quadratic function to tell you whether its reciprocal will have a maximum or minimum.

3.Explain how you can tell the end behaviour of the reciprocal of a quadratic function from the graph of the original quadratic function?

4.Explain how to use the graph of a reciprocal function to solve an inequality.

someone do it fast please i need it tomorrow, please do it.

1. Think about reciprocals. 1/x is smaller if x is larger. So, a max of f(x) is a min for 1/f(x)

2. If the leading coefficient is positive, f(x) has a minimum (the parabola opens upward), and vice-versa for negative.

3. Since a parabola grows without bound, its reciprocal shrinks without bounds - that is, approaches zero.

4. Think of a parabola, with a line drawn across it. If the parabola is above the line, its reciprocal will be below the line.

visit wolframalpha.com and play around with some functions, and see what the graphs look like. Just type in the function and it will display the graph, as well as other information.

thanks

steve can you please email me i have a question for you

steve can you please email me i have a question for you, brar.09hotmai

1. To understand the relationship between the maximum or minimum point of the original quadratic function and its reciprocal function, we need to consider the reciprocal function's graph. The reciprocal function of a quadratic function is obtained by taking the reciprocal of the y-values of the original function at each point.

If the original quadratic function has a maximum point, it means that the graph of the function opens downwards. When we take the reciprocal of the y-values, the graph of the reciprocal function will have a minimum point. Likewise, if the original quadratic function has a minimum point, the reciprocal function's graph will have a maximum point. Therefore, the maximum and minimum points of the original quadratic function are inversely related to each other in the reciprocal function.

2. The leading coefficient of a quadratic function, which is the coefficient of the highest power of x, can tell us whether the reciprocal function will have a maximum or minimum point.

If the leading coefficient is positive (greater than 0), the quadratic function will open upwards and have a minimum point. In this case, the reciprocal function will have a maximum point.

Conversely, if the leading coefficient is negative (less than 0), the quadratic function will open downwards and have a maximum point. In this situation, the reciprocal function will have a minimum point.

In summary, the leading coefficient of the original quadratic function provides insight into the nature (maximum or minimum) of the reciprocal function.

3. The end behavior of a reciprocal function can be determined by analyzing the graph of the original quadratic function.

If the original quadratic function is positive (open upwards), the graph will approach positive infinity as x approaches positive or negative infinity. Therefore, for the reciprocal function, the y-values will approach 0 as x approaches positive or negative infinity. Hence, the end behavior of the reciprocal function will approach the x-axis.

On the other hand, if the original quadratic function is negative (open downwards), the graph will approach negative infinity as x approaches positive or negative infinity. Consequently, for the reciprocal function, the y-values will still approach 0 as x approaches positive or negative infinity. In this case, the reciprocal function's end behavior will also approach the x-axis.

To summarize, the end behavior of the reciprocal function mirrors the end behavior of the original quadratic function by tending towards the x-axis.

4. Using the graph of a reciprocal function, we can solve an inequality by determining the regions where the function is either greater than or less than a given value.

For example, let's say we have the reciprocal function f(x) = 1/x and we want to solve the inequality f(x) > 2. To do this, we look at the graph of f(x) and identify the region(s) where the graph is above the horizontal line y = 2.

Since the reciprocal function f(x) = 1/x is symmetric about the y-axis, we observe that it is positive for both positive and negative x-values. Therefore, we only need to focus on the region where the graph is above y = 2.

By analyzing the graph, we can see that the function f(x) > 2 when x < 1/2 or x > -1/2. These values correspond to the areas where the reciprocal function is above the horizontal line y = 2.

Hence, the solution to the inequality f(x) > 2 is x < 1/2 or x > -1/2, which can be obtained by examining the graph of the reciprocal function.