The vertex form of the equation of a parabola is y = (x - 3)2 + 36.What is the standard form of the equation?A.y = x2 - 6x + 45B.y = x2 + x + 18C.y = 3x2 - 6x + 45D.y = x2 + 6x + 36
Question
The vertex form of the equation of a parabola is y = (x - 3)2 + 36.What is the standard form of the equation?A.y = x2 - 6x + 45B.y = x2 + x + 18C.y = 3x2 - 6x + 45D.y = x2 + 6x + 36
Solution
The standard form of a quadratic equation is given by y = ax^2 + bx + c.
The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Given the vertex form of the equation y = (x - 3)^2 + 36, we can expand it to find the standard form.
First, expand (x - 3)^2. This is equal to x^2 - 6x + 9.
So, y = x^2 - 6x + 9 + 36.
Simplify the equation to get y = x^2 - 6x + 45.
So, the standard form of the equation is y = x^2 - 6x + 45.
Therefore, the answer is A. y = x^2 - 6x + 45.
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