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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, 2, x, squared, minus, 28, x, plus, 80y=2x 2 −28x+80

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, 2, x, squared, minus, 28, x, plus, 80y=2x 2 −28x+80

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Solution

The equation you provided seems to be a bit incorrect. If we are dealing with a parabola, the equation should be in the form y = ax^2 + bx + c.

Assuming the correct equation is y = 2x^2 - 28x + 80, we can find the vertex using the formula for the x-coordinate of the vertex of a parabola, which is -b/2a.

Here, a = 2 and b = -28.

So, the x-coordinate of the vertex is -(-28)/(2*2) = 28/4 = 7.

To find the y-coordinate of the vertex, we substitute x = 7 into the equation:

y = 2*(7)^2 - 287 + 80 = 249 - 196 + 80 = 98 - 196 + 80 = -18.

So, the vertex of the parabola is (7, -18).

This problem has been solved

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