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ACTIVITY: Set Me to Your Standard!

Write each quadratic equation in standard form, [tex]a x^2 + b x + c = 0[/tex], then identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. Answer the questions that follow.

1. [tex]3x - 2x^2 = 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) = -3x[/tex]
7. [tex](x - 4)^2 + 8 = 0[/tex]
8. [tex](x + 2)^2 = 3(x + 2)[/tex]
9. [tex](2x - 1)^2 = (x + 1)^2[/tex]
10. [tex]2x(x + 4) = (x - 3)(x - 3)[/tex]



Answer :

GinnyAnswer
Alright, let's rewrite each quadratic equation in standard form [tex]\[a x^2 + b x + c = 0\][/tex] and identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].

1. Equation: [tex]\( 3x - 2x^2 = 7 \)[/tex]
- Standard form: [tex]\(-2x^2 + 3x - 7 = 0\)[/tex]
- Coefficients: [tex]\( a = -2 \)[/tex], [tex]\( b = 3 \)[/tex], [tex]\( c = -7 \)[/tex]

2. Equation: [tex]\( 5 - 2x^2 = 6x \)[/tex]
- Standard form: [tex]\(-2x^2 - 6x + 5 = 0\)[/tex]
- Coefficients: [tex]\( a = -2 \)[/tex], [tex]\( b = -6 \)[/tex], [tex]\( c = 5 \)[/tex]

3. Equation: [tex]\( (x + 7)(x - 7) = -3x \)[/tex]
- Standard form: [tex]\( x^2 + 3x - 49 = 0 \)[/tex]
- Coefficients: [tex]\( a = 1 \)[/tex], [tex]\( b = 3 \)[/tex], [tex]\( c = -49 \)[/tex]

4. Equation: [tex]\( (x + 3)(x + 4) = 0 \)[/tex]
- Standard form: [tex]\( x^2 + 7x + 12 = 0 \)[/tex]
- Coefficients: [tex]\( a = 1 \)[/tex], [tex]\( b = 7 \)[/tex], [tex]\( c = 12 \)[/tex]

5. Equation: [tex]\( (x - 4)^2 + 8 = 0 \)[/tex]
- Standard form: [tex]\( x^2 - 8x + 24 = 0 \)[/tex]
- Coefficients: [tex]\( a = 1 \)[/tex], [tex]\( b = -8 \)[/tex], [tex]\( c = 24 \)[/tex]

6. Equation: [tex]\( (2x + 7)(x - 1) = 0 \)[/tex]
- Standard form: [tex]\( 2x^2 + 5x - 7 = 0 \)[/tex]
- Coefficients: [tex]\( a = 2 \)[/tex], [tex]\( b = 5 \)[/tex], [tex]\( c = -7 \)[/tex]

7. Equation: [tex]\( (x + 2)^2 = 3(x + 2) \)[/tex]
- Standard form: [tex]\( x^2 + x - 2 = 0 \)[/tex]
- Coefficients: [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], [tex]\( c = -2 \)[/tex]

8. Equation: [tex]\( 2x(x - 3) = 15 \)[/tex]
- Standard form: [tex]\( 2x^2 - 6x - 15 = 0 \)[/tex]
- Coefficients: [tex]\( a = 2 \)[/tex], [tex]\( b = -6 \)[/tex], [tex]\( c = -15 \)[/tex]

9. Equation: [tex]\( (2x - 1)^2 = (x + 1)^2 \)[/tex]
- Standard form: [tex]\( 3x^2 - 6x = 0 \)[/tex]
- Coefficients: [tex]\( a = 3 \)[/tex], [tex]\( b = -6 \)[/tex], [tex]\( c = 0 \)[/tex]

10. Equation: [tex]\( 2x(x + 4) = (x - 3)^2 \)[/tex]
- Standard form: [tex]\( x^2 + 14x - 9 = 0 \)[/tex]
- Coefficients: [tex]\( a = 1 \)[/tex], [tex]\( b = 14 \)[/tex], [tex]\( c = -9 \)[/tex]

These steps provide the standard forms of the given quadratic equations and the identified coefficients.

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