Question

quadratic function is defined by f (x) = (x+2)(x-5).use this function to answer the following two problems a. what are the x-intercepts of this function?(2,0) and (10,0)(-5,0) and (2,0)(-2,0) and (5,0)(-5,0) and (-2,0)b. what is the Y intercept of this function

Answer 1

To answer this question, we can proceed as follows:

Part A

The x-intercepts are the values for x when y = 0. These values pass through the x-axis.

In this case, we have that:

f(x) = (x+2)(x-5) ---> f(x) = y = 0 = (x+2)(x-5)

Then, we have that:

(x+2)(x-5) = 0

To find the values for which this expression is equal to zero, we have that:

x + 2 = 0 or,

x - 5 = 0

Then, the two x-intercepts of this function are:

x + 2 = 0 ---> x = -2

x - 5 = 0 ---> x = 5

Therefore, we have x = -2, and x = 5, and the x-intercepts in coordinates are:

(-2, 0) and (5, 0) (option 3)

Part B

To find the y-intercept(s), we need to have x = 0 in the function. That is, the y-intercept is a value for y when x = 0 (the function passes through the y-axis). Then, we have:

f(x) = (x+2)(x-5) ---> for x = 0, we have:

y = f(0) = (0 + 2)(0 - 5) = 2*(-5) = -10.

Therefore, we have that y = -10, and the y-intercept is (0, -10).