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Activity 6: Set Me to Your Standard!

Write each quadratic equation in standard form [tex]ax^2 + bx + c = 0[/tex]. Then answer the questions that follow.

1. [tex]5x - 2x - 7[/tex]
2. [tex]5 - 2x^2 = 6x[/tex]
3. [tex](x + 3)(x + 4) = 0[/tex]
4. [tex](2x + 7)(x - 1) = 0[/tex]
5. [tex]2x(x - 3) = 15[/tex]
6. [tex](x + 7)(x - 7) = -7x[/tex]
7. [tex](x - 4)^2 + y = 0[/tex]
8. [tex](x + 2) = 3(x + 2)[/tex]
9. [tex](2x - 1) = (x + 1)[/tex]
10. [tex](24x + 4) = (x - 3)(x - ?)[/tex]



Answer :

GinnyAnswer
### Detailed Step-by-Step Solution:

#### Question 1
[tex]\[ 5x - 2x - 7 \][/tex]

Combine like terms:

[tex]\[ 5x - 2x - 7 = 3x - 7 \][/tex]

To convert it to standard form [tex]\(Ax + B = 0\)[/tex]:

[tex]\[ 3x - 7 = 0 \][/tex]

#### Question 2
[tex]\[ 5 - 2x^2 = 6x \][/tex]

Move all terms to one side to set the equation to 0:

[tex]\[ -2x^2 - 6x + 5 = 0 \][/tex]

Therefore, the standard form is:

[tex]\[ -2x^2 - 6x + 5 = 0 \][/tex]

#### Question 3
[tex]\[ (x + 3)(x + 4) = 0 \][/tex]

Expand the left-hand side:

[tex]\[ x^2 + 4x + 3x + 12 = 0 \][/tex]

Combine like terms:

[tex]\[ x^2 + 7x + 12 = 0 \][/tex]

So, the standard form is:

[tex]\[ x^2 + 7x + 12 = 0 \][/tex]

#### Question 4
[tex]\[ (2x + 7)(x - 1) = 0 \][/tex]

Expand the left-hand side:

[tex]\[ 2x^2 - 2x + 7x - 7 = 0 \][/tex]

Combine like terms:

[tex]\[ 2x^2 + 5x - 7 = 0 \][/tex]

Thus, the standard form is:

[tex]\[ 2x^2 + 5x - 7 = 0 \][/tex]

#### Question 5
[tex]\[ 2x(x - 3) = 15 \][/tex]

Expand the equation and move all terms to one side:

[tex]\[ 2x^2 - 6x - 15 = 0 \][/tex]

The standard form is:

[tex]\[ 2x^2 - 6x - 15 = 0 \][/tex]

#### Question 6
[tex]\[ (x + 7)(x - 7) = -7x \][/tex]

Expand and move all terms to one side:

[tex]\[ x^2 - 49 = -7x \][/tex]

Move [tex]\(-7x\)[/tex] to the left side:

[tex]\[ x^2 + 7x - 49 = 0 \][/tex]

So, the standard form is:

[tex]\[ x^2 + 7x - 49 = 0 \][/tex]

#### Question 7
[tex]\[ (x - 4)^2 + y = 0 \][/tex]

Expand the left-hand side:

[tex]\[ x^2 - 8x + 16 + y = 0 \][/tex]

Thus, the standard form remains:

[tex]\[ x^2 - 8x + 16 + y = 0 \][/tex]

#### Question 8
[tex]\[ x + 2 = 3(x + 2) \][/tex]

Distribute and isolate the equation to make it zero:

[tex]\[ x + 2 = 3x + 6 \][/tex]

Move all terms to one side:

[tex]\[ x + 2 - 3x - 6 = 0 \][/tex]

Combine like terms:

[tex]\[ -2x - 4 = 0 \][/tex]

Thus, the standard form is:

[tex]\[ -2x - 4 = 0 \][/tex]

#### Question 9
[tex]\[ 2x - 1 = x + 1 \][/tex]

Equate the two sides and isolate the equation to make it zero:

[tex]\[ 2x - 1 - x - 1 = 0 \][/tex]

Combine like terms:

[tex]\[ x - 2 = 0 \][/tex]

So, the standard form is:

[tex]\[ x - 2 = 0 \][/tex]

#### Question 10
[tex]\[ 2(4x + 4) = x(x - 3) \][/tex]

Expand and move all terms to one side:

[tex]\[ 2(4x + 4) = x^2 - 3x \][/tex]

Distribute on the left-hand side:

[tex]\[ 8x + 8 = x^2 - 3x \][/tex]

Move all terms to one side:

[tex]\[ 8x + 8 - x^2 + 3x = 0 \][/tex]

Combine like terms:

[tex]\[ -x^2 + 11x + 8 = 0 \][/tex]

Therefore, the standard form is:

[tex]\[ -x^2 + 11x + 8 = 0 \][/tex]

### Summary
1. [tex]\( 5x - 2x - 7 \)[/tex] → [tex]\( 3x - 7 = 0 \)[/tex]
2. [tex]\( 5 - 2x^2 = 6x \)[/tex] → [tex]\( -2x^2 - 6x + 5 = 0 \)[/tex]
3. [tex]\( (x + 3)(x + 4) = 0 \)[/tex] → [tex]\( x^2 + 7x + 12 = 0 \)[/tex]
4. [tex]\( (2x + 7)(x - 1) = 0 \)[/tex] → [tex]\( 2x^2 + 5x - 7 = 0 \)[/tex]
5. [tex]\( 2x(x - 3) = 15 \)[/tex] → [tex]\( 2x^2 - 6x - 15 = 0 \)[/tex]
6. [tex]\( (x + 7)(x - 7) = -7x \)[/tex] → [tex]\( x^2 + 7x - 49 = 0 \)[/tex]
7. [tex]\( (x - 4)^2 + y = 0 \)[/tex] → [tex]\( x^2 - 8x + 16 + y = 0 \)[/tex]
8. [tex]\( x + 2 = 3(x + 2) \)[/tex] → [tex]\( -2x - 4 = 0 \)[/tex]
9. [tex]\( 2x - 1 = x + 1 \)[/tex] → [tex]\( x - 2 = 0 \)[/tex]
10. [tex]\( 2(4x + 4) = x(x - 3) \)[/tex] → [tex]\( -x^2 + 11x + 8 = 0 \)[/tex]