Question

homework assignment 3.2: quadratic functions
score: 1/10 answered: 2/10
question 3
put the equation $y = x^2 + 16x + 55$ into the form $y = (x - h)^2 + k$:
answer: $y = $
question help: video written example

Explanation:

Step1: Complete the square for the x-terms

To convert \( y = x^2 + 16x + 55 \) to vertex form \( y=(x - h)^2 + k \), we start by taking the coefficient of \( x \), which is 16. Half of 16 is 8, and squaring 8 gives \( 8^2 = 64 \). We add and subtract this value inside the equation to complete the square:
\( y = x^2 + 16x + 64 - 64 + 55 \)

Step2: Rewrite the perfect square trinomial

The first three terms \( x^2 + 16x + 64 \) form a perfect square trinomial, which can be written as \( (x + 8)^2 \). Now we simplify the constant terms:
\( y=(x + 8)^2 - 64 + 55 \)

Step3: Simplify the constant terms

Calculate \( -64 + 55 \):
\( -64 + 55=-9 \)
So the equation becomes \( y=(x + 8)^2 - 9 \). Since \( (x - h)^2=(x + 8)^2 \) implies \( h=-8 \) and \( k = - 9 \), the vertex form is \( y=(x - (-8))^2+(-9)=(x + 8)^2 - 9 \)

Answer:

\( y=(x + 8)^2 - 9 \)