Question

The zeros of a function are the values of x for which the function is equal to zero. Enter a number in each blank to make true statements about the function h(x)=(2x−2)(x−5).

Answer 1

i) h(x) = 0 when x = 1, and when x = 5

ii) The graph of h intercepts the x-axis at x = 1 and x = 5

iii) The zeros of h are 1 and 5

Explanation:

Question;

From a similar question on the website, we have;

i) h(x) = 0 when x = _, and when x = _

ii) The graph of h intercepts the x-axis at x = _ and x = _

iii) The zeros of h are _ and _

Explanation;

The given function is h(x) = (2·x - 2)·(x - 5)

When h(x) = 0, we have;

h(x) = (2·x - 2)·(x - 5) = 0

Therefore, we have;

(2·x - 2) = 0/(x - 5) = 0

(2·x - 2) = 0

x = 2/2 = 1

x = 1

Where we proceed with (x - 5) = 0/(2·x - 2) = 0, we get;

(x - 5) = 0/(2·x - 2) = 0

(x - 5) = 0

x = 5

Therefore, when h(x) = 0, x = 1, and x = 5

ii) The graph of h intercepts the x-axis at h(x) = 0, at x = 1, and x = 5

Therefore, the graph of h intercepts the x-axis at (1, 0), and (5, 0)

iii) The zeros of h are the values of x for which h(x) = 0, which are x = 1, and x = 5