4.1k views
1 vote
Complete the square to re-write the quadratic function in vertex form.
y=x²+7x+3

User Bao Haojun
by
8.3k points

1 Answer

5 votes

Answer:

To complete the square and rewrite the quadratic function y = x² + 7x + 3 in vertex form, we follow these steps:

Factor out the coefficient of x² from the first two terms:

y = 1(x² + 7x) + 3

Take half of the coefficient of x (which is 7 in this case) and square it. Add this value inside the parentheses, and subtract the same value multiplied by the coefficient of x² (which is 1) outside the parentheses to maintain the same value of the expression:

y = 1(x² + 7x + (7/2)² - (7/2)²) + 3

Simplify inside the parentheses by combining the first three terms using the square of the binomial formula (a + b)² = a² + 2ab + b²:

y = 1(x + 7/2)² - 1/4 + 3

Combine the constant terms to simplify:

y = 1(x + 7/2)² + 11/4

Therefore, the quadratic function y = x² + 7x + 3 can be written in vertex form as y = (x + 7/2)² + 11/4. The vertex is located at the point (-7/2, 11/4).

Hope This Helps!

User Edoardo
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories