Write the following quadratic function in vertex form 𝑦 =1/4 𝑥^2 − 4𝑥 + 5
To write the quadratic function in vertex form, we need to complete the square. To do this, we need to factor out a common factor from the first two terms of the quadratic function:
y = (1/4)x^2 − 4x + 5
= (1/4)(x^2 − 16x) + 5
Next, we need to add and subtract the square of half of the coefficient of the x-term, which is (-4/2)^2 = 4:
y = (1/4)(x^2 − 16x + 4 - 4) + 5
Now, we can rewrite the expression inside the parentheses as a perfect square trinomial:
y = (1/4)(x^2 - 16x + 4) - 1 + 5
Next, we can simplify the expression inside the parentheses by factoring the perfect square trinomial:
y = (1/4)(x - 2)^2 - 1 + 5
Finally, we can simplify the constants:
y = (1/4)(x - 2)^2 + 4
Therefore, the quadratic function in vertex form is y = (1/4)(x - 2)^2 + 4.