lizziefufu2
Answered

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The vertex form of the equation of a parabola is [tex]$y=2(x+3)^2-5$[/tex]. What is the standard form of the equation?

A. [tex]$y=2 x^2+5 x+9$[/tex]

B. [tex][tex]$y=2 x^2+12 x+13$[/tex][/tex]

C. [tex]$x=2 y^2+5 y+9$[/tex]

D. [tex]$y=4 x^2+4 x+4$[/tex]

Sagot :

GinnyAnswer
To convert the vertex form of a parabola to its standard form, we need to follow a series of algebraic steps.

Given the vertex form of the equation:
[tex]\[ y = 2 (x + 3)^2 - 5 \][/tex]

We will expand this equation step-by-step.

1. Expand [tex]\((x + 3)^2\)[/tex]:

[tex]\[ (x + 3)^2 = (x + 3)(x + 3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9 \][/tex]

2. Multiply the expanded expression by 2:

[tex]\[ 2(x^2 + 6x + 9) = 2x^2 + 12x + 18 \][/tex]

3. Subtract 5 from the result:

[tex]\[ 2x^2 + 12x + 18 - 5 = 2x^2 + 12x + 13 \][/tex]

Therefore, the standard form of the equation is:
[tex]\[ y = 2x^2 + 12x + 13 \][/tex]

Hence, the correct answer is:
[tex]\[ \boxed{y = 2 x^2 + 12 x + 13} \][/tex]
Thus, the answer choice is B.
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