Final answer:
To find the x-intercepts of the given quadratic function, rearrange it to form a quadratic equation and use the quadratic formula to solve for the values of x. The x-intercepts of the function q(x) = 2x² - 12x + 17 are approximately x = 3.7071 and x = 2.2929.
Step-by-step explanation:
To determine the x-intercepts of the given function q(x) = 2x² - 12x + 17, we need to find the values of x where the function equals 0. This can be done by setting q(x) = 0 and solving the resulting quadratic equation.
We rearrange the quadratic equation as follows: 2x² - 12x + 17 = 0. Now we can use the quadratic formula to find the x-intercepts:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values from the quadratic equation above, we get:
x = (-(-12) ± √((-12)² - 4(2)(17))) / (2(2))
Simplifying further, we have:
x = (12 ± √(144 - 136)) / 4
x = (12 ± √8) / 4
Now we can simplify the square root and solve for the x-intercepts:
x = (12 ± 2√2) / 4
x = 3 ± 0.7071
Therefore, the x-intercepts of the given function q(x) = 2x² - 12x + 17 are approximately x = 3.7071 and x = 2.2929.