Answer:
y-coordinate = 1
Explanation:
Identifying the form of y = x^2 + 8x + 17:
The equation y = x^2 + 8x + 17 is in the standard form of a quadratic, whose general equation is given by:
y = ax^2 + bx + c, ,where
- a, b, and c are constants.
Thus, for y = x^2 + 8x + 17, 1 is our a value, 8 is our b value, and 17 is our c value.
Using this information to find the y-coordinate of the vertex:
We can first find the x-coordinate of the vertex using the formula -b / 2a.
Thus, we can find the x-coordinate of the vertex by substituting 8 for b and 1 for a:
x-coordinate = -8 / 2(1)
x-coordinate = -8 / 2
x-coordinate = -4
Thus, the x-coordinate of the vertex is -4.
Now we can find the y-coordinate of the vertex by substituting -4 for x in y = x^2 + 8x + 17 and solving for y:
y = (-4)^2 + 8(-4) + 17
y = 16 - 32 + 17
y = -16 + 17
y = 1
Thus, the y-coordinate of the vertex is 1.