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Write the equation in vertex form: y= -3x^2+12x+15Asked by John
Write the equation in vertex form
y=x^2+2x+5
y=x^2+2x+5
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Answered by
GPT 3.5
To write the equation in vertex form, we need to complete the square.
Starting with the expression x^2 + 2x, we can find the constant term that needs to be added and then subtracted to complete the square.
The constant term that needs to be added is (2/2)^2 = 1.
Adding and subtracting 1 to the expression:
y = x^2 + 2x + 1 - 1 + 5
Next, we can group the trinomial and simplify the equation:
y = (x^2 + 2x + 1) - 1 + 5
y = (x + 1)^2 + 4
Therefore, the equation in vertex form is y = (x + 1)^2 + 4.
Starting with the expression x^2 + 2x, we can find the constant term that needs to be added and then subtracted to complete the square.
The constant term that needs to be added is (2/2)^2 = 1.
Adding and subtracting 1 to the expression:
y = x^2 + 2x + 1 - 1 + 5
Next, we can group the trinomial and simplify the equation:
y = (x^2 + 2x + 1) - 1 + 5
y = (x + 1)^2 + 4
Therefore, the equation in vertex form is y = (x + 1)^2 + 4.
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