Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.

Question

y, equals, x, squared, minus, 2, x, plus, 8
y=x
2
−2x+8

Answer 1

To find the vertex of the parabola given by the equation \( y = x^2 - 2x + 8 \), we can use the formula for the x-coordinate of the vertex of a parabola in the form \( y = ax^2 + bx + c \). The x-coordinate of the vertex can be found using \( x = -\frac{b}{2a} \).

Here, the coefficients are:

• \( a = 1 \) (the coefficient of \( x^2 \))
• \( b = -2 \) (the coefficient of \( x \))
• \( c = 8 \) (the constant term)

First, we calculate the x-coordinate of the vertex:

\[ x = -\frac{-2}{2 \cdot 1} = \frac{2}{2} = 1 \]

Next, we find the y-coordinate by substituting \( x = 1 \) back into the equation:

\[ y = (1)^2 - 2(1) + 8 \] \[ y = 1 - 2 + 8 \] \[ y = 7 \]

Thus, the coordinates of the vertex of the parabola are:

\[ \boxed{(1, 7)} \]