Question

Megan wants to find the minimum value of the function y = x^2 - 10x + 3. She begins to convert the equation into vertex form by completing the square. Megan stops at the step below.

y = (x + a)^2 + 3 + b

what number should Megan use to replace the a in this equation?

A. 25

B. -10

C. 100

D. -5​

Answer 1

The equation y = x^2 - 10x + 3 is in standard form

Megan should replace the a in y = (x + a)^2 + 3 + b with -5

How to write the function in vertex form?

The function is given as:

y = x^2 - 10x + 3

Rewrite as:

y = (x^2 - 10x) + 3

Take the coefficient (k) of x

k = -10

Divide by 2

k/2 = -5

Square both sides

(k/2)^2 = 25

So, we have:

y = (x^2 - 10x + 25 - 25) + 3

Rewrite as:

y = (x^2 - 10x + 25) - 25 + 3

Express as a perfect square

y = (x - 5)^2 - 25 + 3

From the question, we have:

y = (x + a)^2 + 3 + b

By comparing both equations, we have:

a = -5

Hence, Megan should replace the a in y = (x + a)^2 + 3 + b with -5

Read more about vertex forms at:

https://brainly.com/question/15914313