Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.y, equals, x, squared, plus, 3y=x 2 +3
Question
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.y, equals, x, squared, plus, 3y=x 2 +3
Solution
The equation you provided seems to be a bit unclear. However, if you're referring to a quadratic function in the form of y = ax^2 + bx + c, the vertex of the parabola can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the function y = ax^2 + bx + c.
If the equation is y = x^2 + 3, the vertex can be found as follows:
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Identify a, b, and c from the equation. Here, a = 1, b = 0 (since there is no x term), and c = 3.
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Plug the values of a and b into the formula -b/2a to find the x-coordinate of the vertex. Here, -b/2a = -0/(2*1) = 0.
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Substitute x = 0 into the equation to find the y-coordinate of the vertex. Here, y = (0)^2 + 3 = 3.
So, the vertex of the parabola y = x^2 + 3 is (0, 3).
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