Question

Исследовать функцию и построить график y=(2x-1)(x+1)

Answer 1

По приложению вроде так. смотри прикрепленный файл

Answer 2

Function Analysis and Graph of y=(2x-1)(x+1)

To analyze the function y=(2x-1)(x+1) and plot its graph, we can start by expanding the equation:

y = (2x-1)(x+1)

Expanding the equation gives us:

y = 2x^2 + 2x - x - 1

Simplifying further, we have:

y = 2x^2 + x - 1

Now, let's plot the graph of this function.

To plot the graph, we can use the x and y-intercepts, as well as the shape of the quadratic function.

X-intercepts:

To find the x-intercepts, we set y=0 and solve for x:

0 = 2x^2 + x - 1

Using the quadratic formula, we can find the x-intercepts:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = 1, and c = -1. Plugging these values into the quadratic formula, we get:

x = (-1 ± √(1^2 - 4(2)(-1))) / (2(2))

Simplifying further, we have:

x = (-1 ± √(1 + 8)) / 4

x = (-1 ± √9) / 4

x = (-1 ± 3) / 4

This gives us two x-intercepts:

x = (-1 + 3) / 4 = 2 / 4 = 0.5

x = (-1 - 3) / 4 = -4 / 4 = -1

So, the x-intercepts of the graph are x = 0.5 and x = -1.

Y-intercept:

To find the y-intercept, we set x=0 and solve for y:

y = 2(0)^2 + (0) - 1

Simplifying, we get:

y = -1

So, the y-intercept of the graph is y = -1.

Shape of the Graph:

Since the leading coefficient of the quadratic term (x^2) is positive (2 > 0), the graph opens upwards. This means that the graph will have a minimum point.

Plotting the Graph:

Now, let's plot the graph of y=(2x-1)(x+1) using the information we have gathered.

The x-intercepts are x = 0.5 and x = -1, and the y-intercept is y = -1. The graph opens upwards and has a minimum point.

Here is the graph:


Please note that the graph is a rough representation and may not be perfectly accurate. It is always recommended to use graphing software or a graphing calculator for precise graphs.

I hope this helps! Let me know if you have any further questions.