3.3 Notes Part 1_Alg2 Lesson

6 Slides • 7 Questions

1

3.3 Notes Part 1

Perfect Square Trinomials

Completing the Square

2

Multiple Choice

Solve for x:

(x + 6)²= 49

1

x=7,12

2

x=±7

3

x=1,-13

4

x=43,-55

3

Solution

\left(x+6\right)^2=49

\sqrt{\left(x+6\right)^2}=\sqrt{49}

x+6\ =\ \pm7

x+6=7\ \ or\ \ x+6=-7

x=1\ \ or\ \ x=-13

4

(x + 6)² = 49 can be written as:

(x + 6)(x + 6) = 49

use F.O.I.L to get

x² + 12x + 36 = 49

The right side of the equation is a perfect square trinomial

because x² + 12x + 36 can be written as a factor squared, (x + 6)²

If asked to solve x² + 12x + 36 = 49, factor and solve using square roots

5

Recognize PSTs with this formula

6

Multiple Choice

Is this a perfect square trinomial?
x² + 16x + 64

1

Yes

2

No

7

Multiple Choice

Factor: x² + 16x + 64

1

(x + 4)²

2

(x + 8)²

3

(x + 16)²

8

Multiple Choice

Solve x² + 16x + 64 = 25 using square roots

1

x = -3, -13

2

x = -3, 3

3

x = -13, 13

4

x = 5, 8

9

Solution

x^2+16x+64\ =\ 25

\left(x+8\right)^2=25

\sqrt{\left(x+8\right)^2}=\sqrt{25}

x+8\ =\ \pm5

x+8=5\ \ or\ \ x+8=-5

x=-3\ \ or\ \ x=-13

10

Multiple Choice

Is this a perfect square trinomial?
x² + 18x + 9

1

Yes

2

No

11

Multiple Choice

Is this a perfect square trinomial?

x² - 14x + 49

1

Yes

2

No

12

Multiple Choice

Solve: $x^2-14x+49=-2$

1

x = -9, 5

2

x = -7, 7

3

$x=7\pm2i$

4

$x=7\pm i\sqrt{2}$

13

Solve:

x^2-14x+49=-2

$\left(x-7\right)^2=-2$
$\sqrt{\left(x-7\right)^2}=\sqrt{-2}$
$x-7=\pm\sqrt{-2}$
$x-7=\pm i\sqrt{2}$
$x=7\pm i\sqrt{2}$

3.3 Notes Part 1

Perfect Square Trinomials

Completing the Square

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