Question

use your graphing calculator to sketch the graph of the function, and then determine the coordinates of the x-intercepts for the function, if they exist.
( g(x) = -x^2 + 11x - 18 )

sketch the graph of the function in the viewing window (-10,10 \times -15,15). choose the correct graph below.
a.

b.

c

d.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the x-intercept(s) is(are)
(type an ordered pair. use a comma to separate answers as needed. use integers or decimals for any numbers in the expression.)
b. there are no x-intercepts.

Explanation:

Step1: Find x-intercepts by setting \( g(x) = 0 \)

Set \( -x^2 + 11x - 18 = 0 \). Multiply both sides by -1: \( x^2 - 11x + 18 = 0 \).

Step2: Factor the quadratic equation

Factor \( x^2 - 11x + 18 \). We need two numbers that multiply to 18 and add to -11. The numbers are -2 and -9. So, \( (x - 2)(x - 9) = 0 \).

Step3: Solve for x

Set each factor equal to zero: \( x - 2 = 0 \) or \( x - 9 = 0 \). Thus, \( x = 2 \) or \( x = 9 \).

Step4: Write x-intercepts as ordered pairs

The x-intercepts occur where \( y = 0 \), so the ordered pairs are \( (2, 0) \) and \( (9, 0) \).

Answer:

The x-intercept(s) is(are) \((2, 0)\), \((9, 0)\)