Question
Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the vertex form of the equation?
y=−x^2+6x−7
(3 points)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the vertex form of the equation?
y=−x^2+6x−7
(3 points)
Answers
Answered by
GPT 3.5
To find the vertex form of the equation, we need to complete the square.
Step 1: Rewrite the equation by factoring out the coefficient of x^2 from the first two terms:
y = -(x^2 - 6x) - 7
Step 2: Take the coefficient of x, divide it by 2, and then square it. Add this result inside the parentheses, and subtract the same value outside the parentheses to keep the equation balanced. In this case, the coefficient of x is -6, so (-6/2)^2 = (-3)^2 = 9.
y = -(x^2 - 6x + 9 - 9) - 7
Step 3: Rearrange the equation by grouping the squared term and the constant term together, and factor the quadratic inside the parentheses:
y = -(x^2 - 6x + 9) + 9 - 7
y = -(x - 3)^2 + 2
The vertex form of the equation is y = -(x - 3)^2 + 2.
Step 1: Rewrite the equation by factoring out the coefficient of x^2 from the first two terms:
y = -(x^2 - 6x) - 7
Step 2: Take the coefficient of x, divide it by 2, and then square it. Add this result inside the parentheses, and subtract the same value outside the parentheses to keep the equation balanced. In this case, the coefficient of x is -6, so (-6/2)^2 = (-3)^2 = 9.
y = -(x^2 - 6x + 9 - 9) - 7
Step 3: Rearrange the equation by grouping the squared term and the constant term together, and factor the quadratic inside the parentheses:
y = -(x^2 - 6x + 9) + 9 - 7
y = -(x - 3)^2 + 2
The vertex form of the equation is y = -(x - 3)^2 + 2.
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