141k views
3 votes
3x^2+16x+20 vertex form

User Rkt
by
8.0k points

1 Answer

6 votes

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

User Hearty
by
8.0k points

No related questions found