# Eureka Math Algebra 1 Module 4 Lesson 11 Answer Key

## Engage NY Eureka Math Algebra 1 Module 4 Lesson 11 Answer Key

### Eureka Math Algebra 1 Module 4 Lesson 11 Example Answer Key

Example
Now try working backward. Rewrite the following standard form quadratic expressions as perfect squares.

### Eureka Math Algebra 1 Module 4 Lesson 11 Exploratory Challenge Answer Key

Exploratory Challenge
Find an expression equivalent to x2 + 8x + 3 that includes a perfect square binomial.
(x + 4)2 – 13

### Eureka Math Algebra 1 Module 4 Lesson 11 Exercise Answer Key

Opening Exercise
Rewrite the following perfect square quadratic expressions in standard form. Describe patterns in the coefficients for the factored form, (x + A)2, and the standard form, x2 + bx + c.

For each row, the factored form and standard form are equivalent expressions, so (x + A)2=x2 + bx + c. A, the constant in factored form of the equation, is always half of b, the coefficient of the linear term in the standard form. c, the constant term in the standard form of the quadratic equation, is always the square of the constant in the factored form, A.

Exercises
Rewrite each expression by completing the square.
Exercise 1.
a2 – 4a + 15
(a – 2)2 + 11
(Note: Since the constant term required to complete the square is less than the constant term, + 15, students may notice that they just need to split the + 15 strategically.)

Exercise 2.
n2 – 2n – 15
(n – 1)2 – 16

Exercise 3.
c2 + 20c – 40
(c + 10)2 – 140

Exercise 4.
x2 – 1000x + 60 000
(x – 500)2 – 190 000

Exercise 5.
y2 – 3y + 10
(y – $$\frac{3}{2}$$)2 + $$\frac{31}{4}$$

Exercise 6.
k2 + 7k + 6
(k + $$\frac{7}{2}$$)2 – $$\frac{25}{4}$$

Exercise 7.
z2 – 0.2z + 1.5
(z – 0.1)2 + 1.49

Exercise 8.
p2 + 0.5p + 0.1
(p + 0.25)2 + 0.0375

Exercise 9.
j2 – $$\frac{3}{4}$$ j + $$\frac{3}{4}$$
(j – $$\frac{3}{8}$$)2 + $$\frac{39}{64}$$

Exercise 10.
x2 – bx + c
(x – $$\frac{b}{2}$$)2 + c – $$\frac{b^{2}}{4}$$

### Eureka Math Algebra 1 Module 4 Lesson 11 Problem Set Answer Key

Rewrite each expression by completing the square.
Question 1.
q2 + 12q + 32
(q + 6)2 – 4

Question 2.
m2 – 4m – 5
(m – 2)2 – 9

Question 3.
x2 – 7x + 6.5
(x – $$\frac{7}{2}$$)2 – 5.75

Question 4.
a2 + 70a + 1225
(a + 35)2

Question 5.
z2 – 0.3z + 0.1
(z – 0.15)2 + 0.0775

Question 6.
y2 – 6by + 20
(y – 3b)2 + 20 – 9b2

Question 7.
Which of these expressions would be most easily rewritten by factoring? Justify your answer.