convert to vertex form
𝑦 =1/4𝑥^2 − 4𝑥 + 5
To convert the given equation to vertex form, we need to complete the square.
The equation 𝑦 = 1/4𝑥^2 - 4𝑥 + 5 can be rewritten as:
𝑦 = (1/4)(𝑥^2 - 16𝑥) + 5
Now, let's complete the square inside the parentheses:
𝑦 = (1/4)(𝑥^2 - 16𝑥 + 64 - 64) + 5
= (1/4)((𝑥 - 8)^2 - 64) + 5
Next, distribute the 1/4 to the terms inside the parentheses:
𝑦 = (1/4)(𝑥 - 8)^2 - 16 + 5
= (1/4)(𝑥 - 8)^2 - 11
Thus, the vertex form of the given equation is 𝑦 = (1/4)(𝑥 - 8)^2 - 11.