Lesson 3 Building the Perfect Square Develop Understanding

Ready

Find the $x$ -intercept and the $y$ -intercept, then graph the equation.

1.

$3 x + 2 y = 12$

$x$ -intercept:

$y$ -intercept:

2.

$8 x - 12 y = - 24$

$x$ -intercept:

$y$ -intercept:

3.

$y = \frac{3}{7} x - 3$

$x$ -intercept:

$y$ -intercept:

Set

Rewrite each expression as an equivalent trinomial.

4.

$(x + 5) (x + 5)$

5.

$(x + 7) (x + 7)$

6.

${(x + 9)}^{2}$

7.

${(x + 11)}^{2}$

8.

Write a rule for finding the coefficient, $b$ , of standard form, $a x^{2} + b x + c$ , when multiplying and combining like terms for an expression in the format ${(x + q)}^{2}$ .

In problems 9–14,

Fill in the number that creates a perfect square.
Then, write the trinomial as the square of a binomial.

9.

a.

$x^{2} + 8 x +$

b.

Square of a binomial:

10.

a.

$x^{2} + 10 x +$

b.

Square of a binomial:

11.

a.

$x^{2} + 16 x +$

b.

Square of a binomial:

12.

a.

$x^{2} + 6 x +$

b.

Square of a binomial:

13.

a.

$x^{2} + 22 x +$

b.

Square of a binomial:

14.

a.

$x^{2} + 18 x +$

b.

Square of a binomial:

In problems 15–23,

Find the value of $B$ that will make a perfect square trinomial.
Then, write the trinomial as the square of a binomial.

15.

$x^{2} + B x + 16$

a.

$B =$

b.

Square of a binomial:

16.

$x^{2} + B x + 121$

a.

$B =$

b.

Square of a binomial:

17.

$x^{2} + B x + 625$

a.

$B =$

b.

Square of a binomial:

18.

$x^{2} + B x + 225$

a.

$B =$

b.

Square of a binomial:

19.

$x^{2} + B x + 49$

a.

$B =$

b.

Square of a binomial:

20.

$x^{2} + B x + 169$

a.

$B =$

b.

Square of a binomial:

21.

$x^{2} + B x + \frac{25}{4}$

a.

$B =$

b.

Square of a binomial:

22.

$x^{2} + B x + \frac{9}{4}$

a.

$B =$

b.

Square of a binomial:

23.

$x^{2} + B x + \frac{49}{4}$

a.

$B =$

b.

Square of a binomial:

Go

Each of the equations below has just one intercept; find it and state whether it’s an $x$ - or $y$ -intercept.

24.

$y = - 4.5$

25.

$x = 9.5$

26.

$x = - 8.2$

27.

$y = 112$