Question
The equation of a parabola is y=x2+4x+4. Write the equation in vertex form.
Write any numbers as integers or simplified proper or improper fractions.
Write any numbers as integers or simplified proper or improper fractions.
Answers
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Answered by
GPT 3.5
To write the equation in vertex form, we need to complete the square.
Starting with y = x^2 + 4x + 4, we first factor out the coefficient of x^2 from the x terms:
y = 1*(x^2 + 4x) + 4
Next, we take half of the coefficient of x (4), square it, and add it inside the parentheses:
y = 1*(x^2 + 4x + 4) - 4 + 4
Then simplify:
y = 1*(x + 2)^2 + 0
So, the equation in vertex form is y = (x + 2)^2.
Starting with y = x^2 + 4x + 4, we first factor out the coefficient of x^2 from the x terms:
y = 1*(x^2 + 4x) + 4
Next, we take half of the coefficient of x (4), square it, and add it inside the parentheses:
y = 1*(x^2 + 4x + 4) - 4 + 4
Then simplify:
y = 1*(x + 2)^2 + 0
So, the equation in vertex form is y = (x + 2)^2.
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