Answered

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Write the quadratic equation in standard form.

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

A. [tex]\( x^2 - 6x + 9 = 0 \)[/tex]
B. [tex]\( x^2 + 6x + 9 = 0 \)[/tex]
C. [tex]\( x^2 + 9 = 0 \)[/tex]

Sagot :

GinnyAnswer
Let's write the quadratic equation [tex]\((x - 3)^2\)[/tex] in standard form. The standard form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are constants.

1. Start with the given equation:
[tex]\[ (x - 3)^2 = 0 \][/tex]

2. Expand the expression [tex]\((x - 3)^2\)[/tex]:
[tex]\[ (x - 3)(x - 3) \][/tex]

3. Apply the distributive property (also known as the FOIL method for binomials) to expand the expression:
[tex]\[ (x - 3)(x - 3) = x^2 - 3x - 3x + 9 \][/tex]

4. Combine like terms:
[tex]\[ x^2 - 3x - 3x + 9 = x^2 - 6x + 9 \][/tex]

Therefore, the quadratic equation in standard form is:
[tex]\[ x^2 - 6x + 9 = 0 \][/tex]
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