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1. Write [tex]\( y = 2x^2 + 8x + 3 \)[/tex] in vertex form.

A. [tex]\( y = 2(x - 2)^2 - 5 \)[/tex]
B. [tex]\( y = (x + 4)^2 + 3 \)[/tex]
C. [tex]\( y = (x - 4)^2 + 3 \)[/tex]
D. [tex]\( y = 2(x + 2)^2 - 5 \)[/tex]

Sagot :

GinnyAnswer
To write the given quadratic equation [tex]\( y = 2x^2 + 8x + 3 \)[/tex] in vertex form, we proceed as follows:

1. Start with the given equation:
[tex]\[ y = 2x^2 + 8x + 3 \][/tex]

2. Factor out the coefficient of [tex]\( x^2 \)[/tex] from the first two terms:
[tex]\[ y = 2(x^2 + 4x) + 3 \][/tex]

3. Complete the square inside the parentheses:
- To complete the square, we need to add and subtract a term inside the parentheses that makes the quadratic expression a perfect square.
- The term we need to add and subtract is [tex]\( (4 / 2)^2 = 4 \)[/tex].

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

4. Distribute the 2 and simplify:
[tex]\[ y = 2(x + 2)^2 - 8 + 3 \][/tex]
[tex]\[ y = 2(x + 2)^2 - 5 \][/tex]

So, the given quadratic equation in vertex form is:
[tex]\[ y = 2(x + 2)^2 - 5 \][/tex]

Hence, the correct answer is:
[tex]\[ y = 2(x + 2)^2 - 5 \][/tex]
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