Answer:
Step-by-step explanation:
Given the vertex form of the quadratic function:
g(x) = - ½(x - 2)² + 5
Transform the vertex form of the quadratic function into its standard form, ax² + bx + c :
g(x) = - ½(x - 2)² + 5
g(x) = - ½x² - 2(- ½)(2)x + - ½(2)² + 5
g(x) = - ½x² - 2(- ½)(2)x - 2 + 5
g(x) = - ½x² + 2x + 3 (Standard form)
where a = - ½, b = 2, and c = 3
In vertex form, we can say, x = h since the axis of symmetry and vertex lies on the same line.
To find the x-coordinate (h ) of the vertex:
[tex]x = \frac{-b}{2a} = \frac{-2}{2(-\frac{1}{2}) } = \frac{-2}{-1} = 2[/tex]
Substitute the value of the x-coordinate (h ) of the vertex into the standard form to find the value of the y-coordinate, (k ):
k = - ½x² + 2x + 3
k = - ½(2)² + 2(2) + 3
k = -2 + 4 + 3 = 5
Therefore, the vertex (h, k) = (2, 5).
