Answer:
To find two points on the graph of the function f(x) = x² - 8x + 8 when f(x) = -4, we can set up the equation and solve for x:
1. Set f(x) equal to -4:
-4 = x² - 8x + 8
2. Rearrange the equation to form a quadratic equation:
x² - 8x + 8 + 4 = 0
3. Combine like terms:
x² - 8x + 12 = 0
4. Solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 1, b = -8, and c = 12.
x = (8 ± √((-8)² - 4(1)(12))) / (2(1))
x = (8 ± √(64 - 48)) / 2
x = (8 ± √16) / 2
x = (8 ± 4) / 2
5. Now, calculate the two possible values of x:
- x₁ = (8 + 4) / 2 = 12 / 2 = 6
- x₂ = (8 - 4) / 2 = 4 / 2 = 2
6. We have found two values of x, which correspond to the x-coordinates of points on the graph when f(x) = -4. Now, plug these values back into the original function to find the corresponding y-coordinates:
- For x = 6:
f(6) = 6² - 8(6) + 8 = 36 - 48 + 8 = -4
- For x = 2:
f(2) = 2² - 8(2) + 8 = 4 - 16 + 8 = -4
So, the two points on the graph of the function f(x) = x² - 8x + 8 when f(x) = -4 are (6, -4) and (2, -4).