F(x) questions about algebra 2

Question

If F(x) = x-5x-14, find all the values of K so that F(k-3)=0

Answer 1

Is this supposed to be x² - 5x - 14?

x² - 5x - 14 = (x + 2)(x - 7) = 0

x = -2 and x = 7

These two values represent the x-intercepts of the graph of f, which is a parabola.

The function f(k - 3) has been shifted three units horizontally to the right. That means the x-intercepts of the graph of f(k - 3) are x = 1 and x = 10.

Answer 2

1) Find zeroes of function

x^2-5x-14=0

factor into (x-7) and (x+2) because -7 and 2 add to -5 and multiply to -14

therefore x-7=0 and x+2=0

that tells us that the zeroes of the function are x=7 and x=-2

2) Find k

need to find k such that k-3=7 and k-3=-2

k-3=7 --> k=10

k-3=-2 --> k=1

3) Answer

There are two possible values of k: k=1 and k=10

Answer 3

F(x) = x - 5x - 14

= -4x - 14

0 = F(k-3) = -4(k-3) - 14

14 = -4(k-3)

14 = -4k + 12

2 = -4k

k = -1/2

k-3 = -1/2 - 3 = -3 and 1/2 = -3.5

F(-3.5)= -4(-3.5) -14

= -14 - 14

= -24