Final answer:
The coordinates of the vertex for the equation y = x² - 12x + 46 are found using the vertex formula x = -b/(2a). The vertex is at point (6, 10).
Step-by-step explanation:
The equation given is y = x² - 12x + 46, which is a quadratic equation in standard form. To find the vertex of the parabola represented by this equation, we can use the formula x = -b/(2a) to find the x-coordinate of the vertex, where a and b are coefficients from the quadratic equation in the form ax² + bx + c. In our equation, a = 1 and b = -12.
Inserting these values into the formula gives us:
x = -(-12)/(2×1)
x = 12/2
x = 6
Now that we have the x-coordinate of the vertex, we can substitute it back into the original equation to find the y-coordinate:
y = (6)² - 12×6 + 46
y = 36 - 72 + 46
y = 10
Therefore, the coordinates of the vertex are (6, 10).