Final answer:
The coordinates of the turning point of the quadratic curve x² - 8x + 19 are found using the formula -b/(2a) for the x-coordinate, and substituting it back into the equation to find the y-coordinate. The turning point is at (4, -5).
Step-by-step explanation:
The question is asking to find the coordinates of the turning point of the quadratic curve defined by the equation x² - 8x + 19.
Steps to Find the Turning Point
- Write the equation in the standard quadratic form, which is ax² + bx + c.
- Use the formula -b/(2a) to find the x-coordinate of the turning point.
- Substitute the x-coordinate back into the original equation to find the corresponding y-coordinate.
In this case, a = 1, b = -8, and c = 19. The x-coordinate of the turning point is -(-8)/(2×1) = 4. Plugging x = 4 into the original equation gives the y-coordinate, which is 4² - 8×4 + 19 = -5. Therefore, the coordinates of the turning point are (4, -5).