Find the zeros of each function. Then graph the function.
y= (x-1) (x+2)
Can you show me how to do this please?
y is zero when x is 1, or x is -2
Sure! To find the zeros of a function, set the function equal to zero and solve for x.
In this case, the function is y = (x - 1)(x + 2). To find the zeros, you set y equal to zero:
0 = (x - 1)(x + 2)
To solve this equation, you can use the zero product property, which states that if two factors multiply to zero, then at least one of the factors must be zero. So, you can set each factor equal to zero and solve for x:
x - 1 = 0 or x + 2 = 0
Solving each equation gives you:
x = 1 or x = -2
Hence, the zeros of the function are x = 1 and x = -2.
To graph the function, you can start by plotting these zeros on the x-axis. For x = 1, you would plot a point at (1, 0), and for x = -2, you would plot a point at (-2, 0).
Since the given function is in the form of a quadratic equation (quadratic trinomial) with no other factors, it represents a parabola. The zeros represent the x-intercepts of the graph.
You can plot a few more points by substituting different x-values into the function and calculating the corresponding y-values. For example, you could substitute x = -1, x = 0, and x = 2:
For x = -1:
y = (-1 - 1)(-1 + 2) = (-2)(1) = -2
So, you would plot the point (-1, -2).
For x = 0:
y = (0 - 1)(0 + 2) = (-1)(2) = -2
So, you would plot the point (0, -2).
For x = 2:
y = (2 - 1)(2 + 2) = (1)(4) = 4
So, you would plot the point (2, 4).
Once you have plotted these points, you can sketch a smooth curve through them to represent the graph of the function y = (x - 1)(x + 2). The shape of the parabola will vary depending on the values of the coefficients in front of x^2 and x, but it will always go through the zeros you found.
I hope this helps! Let me know if you have any more questions.