Findthevertexoftheparabolay = x2.Simplify both coordinates and write them as proper fractions, improper fractions, or integers.
Question
Findthevertexoftheparabolay = x2.Simplify both coordinates and write them as proper fractions, improper fractions, or integers.
Solution 1
The vertex of a parabola given by the equation y = ax^2 + bx + c is found using the formula (-b/2a, f(-b/2a)).
In the equation y = x^2, a = 1, b = 0, and c is not present, which means c = 0.
So, the x-coordinate of the vertex is -b/2a = -0/(2*1) = 0.
Substitute x = 0 into the equation to find the y-coordinate of the vertex: y = (0)^2 = 0.
So, the vertex of the parabola y = x^2 is (0, 0). Both coordinates are integers.
Solution 2
The vertex of a parabola given by the equation y = ax^2 + bx + c is given by the point (-b/2a, c - b^2/4a).
For the equation y = x^2, we can see that a = 1, b = 0, and c = 0.
So, the x-coordinate of the vertex is -b/2a = -0/(2*1) = 0.
The y-coordinate of the vertex is c - b^2/4a = 0 - 0^2/(4*1) = 0.
So, the vertex of the parabola y = x^2 is (0, 0). Both coordinates are integers.
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