To complete the square of the given quadratic equation, we need to rewrite it in the form:
У = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Starting with the given equation:
У = -x^2 + 8x + 7
To complete the square, we look at the coefficient of the x-term, which is 8.
We take half of this coefficient, square it, and add it to both sides of the equation:
У + 64 = -x^2 + 8x + 64 + 7
Simplifying this equation further, we get:
У + 64 = -(x^2 - 8x + 8^2) + 71
Next, we can rewrite the x-term as a perfect square trinomial:
У + 64 = -(x - 4)^2 + 71
Moving the constant term to the other side of the equation, we have:
У = -(x - 4)^2 + 7
Now we can see that the equation is in the desired form, and we can easily identify the vertex and axis of symmetry.
The vertex of the parabola is (h, k) = (4, 7).
The axis of symmetry is the vertical line passing through the vertex, which in this case is x = 4.
Complete the square to determine the vertex and axis of symmetry of
У = -x^ + 8x + 7.
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