Answered

ACTIVITY #2: Write each quadratic equation in standard form, then identify the values of [tex]$a$[/tex], [tex]$b$[/tex], and [tex]$c$[/tex].

1. [tex]$3m^2 + 2m = 7$[/tex]

2. [tex]$6(x-8)(x-1) = -7$[/tex]

3. [tex]$3x^2 - 6 = -2x$[/tex]

4. [tex]$x^2 = 81$[/tex]

5. [tex]$3x^2 = -3x + 2$[/tex]

6. [tex]$4m^2 + 3m = 1$[/tex]

7. [tex]$(x+2)(x+9) = 0$[/tex]

8. [tex]$4x^2 - 9 = -3x$[/tex]

9. [tex]$(x+7)(x-3) = 0$[/tex]

10. [tex]$x^2 = -4x + 9$[/tex]



Answer :

GinnyAnswer
Let's go through each of the given quadratic equations to rewrite them in standard form [tex]\(ax^2 + bx + c = 0\)[/tex], then identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].

### 1. [tex]\(3m^2 + 2m = 7\)[/tex]
To convert this to standard form, we need to move all terms to one side:

[tex]\[ 3m^2 + 2m - 7 = 0 \][/tex]

Here:
- [tex]\(a = 3\)[/tex]
- [tex]\(b = 2\)[/tex]
- [tex]\(c = -7\)[/tex]

### 2. [tex]\(6 \cdot (x-8)(x-1) = -7\)[/tex]
First, simplify and expand the left side:

[tex]\[ 6 \cdot (x-8)(x-1) = 6[x^2 - x - 8x + 8] = 6[x^2 - 9x + 8] = 6x^2 - 54x + 48 \][/tex]

Then, move [tex]\(-7\)[/tex] to the left side:

[tex]\[ 6x^2 - 54x + 48 + 7 = 0 \][/tex]
[tex]\[ 6x^2 - 54x + 55 = 0 \][/tex]

Here:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = -54\)[/tex]
- [tex]\(c = 55\)[/tex]

### 3. [tex]\(3x^2 - 6 = -2x\)[/tex]
Move [tex]\(-2x\)[/tex] to the left side:

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

Here:
- [tex]\(a = 3\)[/tex]
- [tex]\(b = 2\)[/tex]
- [tex]\(c = -6\)[/tex]

### 4. [tex]\(x^2 = 81\)[/tex]
Move [tex]\(81\)[/tex] to the left side:

[tex]\[ x^2 - 81 = 0 \][/tex]

Here:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 0\)[/tex]
- [tex]\(c = -81\)[/tex]

### 5. [tex]\(3x^2 = -3x + 2\)[/tex]
Move [tex]\(-3x\)[/tex] and [tex]\(2\)[/tex] to the left side:

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

Here:
- [tex]\(a = 3\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -2\)[/tex]

### 6. [tex]\(4m^2 + 3m = 1\)[/tex]
Move [tex]\(1\)[/tex] to the left side:

[tex]\[ 4m^2 + 3m - 1 = 0 \][/tex]

Here:
- [tex]\(a = 4\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -1\)[/tex]

### 7. [tex]\((x+2)(x+9) = 0\)[/tex]
Expand the left side:

[tex]\[ x(x + 9) + 2(x + 9) = x^2 + 9x + 2x + 18 = x^2 + 11x + 18 = 0 \][/tex]

Here:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 11\)[/tex]
- [tex]\(c = 18\)[/tex]

### 8. [tex]\(4x^2 - 9 = -3x\)[/tex]
Move [tex]\(-3x\)[/tex] to the left side:

[tex]\[ 4x^2 + 3x - 9 = 0 \][/tex]

Here:
- [tex]\(a = 4\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -9\)[/tex]

### 9. [tex]\(5(x+7)(x-3) = 0\)[/tex]
Expand the left side:

[tex]\[ 5[x(x-3) + 7(x-3)] = 5[x^2 - 3x + 7x - 21] = 5[x^2 + 4x - 21] = 5x^2 + 20x - 105 = 0 \][/tex]

Here:
- [tex]\(a = 5\)[/tex]
- [tex]\(b = 20\)[/tex]
- [tex]\(c = -105\)[/tex]

### 10. [tex]\(x^2 = -4x + 9\)[/tex]
Move [tex]\(-4x\)[/tex] and [tex]\(9\)[/tex] to the left side:

[tex]\[ x^2 + 4x - 9 = 0 \][/tex]

Here:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 4\)[/tex]
- [tex]\(c = -9\)[/tex]

## Summary

| Equation | Standard Form | [tex]\(a\)[/tex] | [tex]\(b\)[/tex] | [tex]\(c\)[/tex] |
|----------|---------------------------|--------|--------|--------|
| 1 | [tex]\(3m^2 + 2m - 7 = 0\)[/tex] | 3 | 2 | -7 |
| 2 | [tex]\(6x^2 - 54x + 55 = 0\)[/tex] | 6 | -54 | 55 |
| 3 | [tex]\(3x^2 + 2x - 6 = 0\)[/tex] | 3 | 2 | -6 |
| 4 | [tex]\(x^2 - 81 = 0\)[/tex] | 1 | 0 | -81 |
| 5 | [tex]\(3x^2 + 3x - 2 = 0\)[/tex] | 3 | 3 | -2 |
| 6 | [tex]\(4m^2 + 3m - 1 = 0\)[/tex] | 4 | 3 | -1 |
| 7 | [tex]\(x^2 + 11x + 18 = 0\)[/tex] | 1 | 11 | 18 |
| 8 | [tex]\(4x^2 + 3x - 9 = 0\)[/tex] | 4 | 3 | -9 |
| 9 | [tex]\(5x^2 + 20x - 105 = 0\)[/tex] | 5 | 20 | -105 |
| 10 | [tex]\(x^2 + 4x - 9 = 0\)[/tex] | 1 | 4 | -9 |

These are the quadratic equations in standard form along with their respective values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].

Other Questions