Answer:
the vertex form of the given quadratic expression is:
y = 3(x + 8/3)^2 - 4/3
Explanation:
To write the given quadratic expression 3x^2+16x+20 in vertex form, we need to complete the square.
Step 1: Factor out the coefficient of x^2:
3(x^2 + (16/3)x) + 20
Step 2: Take half of the coefficient of x and square it:
(16/3)/2 = 8/3
(8/3)^2 = 64/9
Step 3: Add and subtract the result from step 2 inside the parentheses:
3(x^2 + (16/3)x + 64/9 - 64/9) + 20
Step 4: Simplify inside the parentheses and factor:
3[(x + 8/3)^2 - 64/9] + 20
Step 5: Simplify the constant term:
3(x + 8/3)^2 - 4/3
Therefore, the vertex form of the given quadratic expression is:
y = 3(x + 8/3)^2 - 4/3