Find the vertex of this parabola:
y=-x2 + 2x-7

the vertex as a whole is (1, -6)

Step-by-step explanation:

Please write y=-x2 + 2X-7  as   y= -x^2 + 2x - 7.  The " ^ " symbol indicates exponentiation.  Because the first term is negative, we know that the parabola opens down, which makes the vertex the maximum of this function.

The axis of symmetry passes through the vertex.  The formula for this axis is:

         -b                                                         -(2)

x =    and the x-value here is   x = = 1

        2a                                                         2(-1)

Use synthetic division with divisor 1 to determine the y-coordinate of the vertex:

1      -1     2     -7

              -1      1

        -1      1     -6

The remainder is -6.  That means that the y-coordinate of the vertex is -6, so that the vertex as a whole is (1, -6).

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

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step-by-step explanation:

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