Determine the Vertex and the x intercepts for the function:   y = -2(x - 1)^2 + 24 a)  v(1, 24); 13, -11 b)  v(1, -24); 13, -11 c)  v(1, 24); none d)  v(1, 24); 1+ 2sqrt(3), 1 - 2sqrt(3) e)  v(1, -24); 1 + 2sqrt(3), 1 - 2sqrt(3) f)  v(1, -24); none

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Determine the vertex and the x-intercepts for the function


This is in vertex form `y=a(x-h)^2+k` where the vertex is at (h,k). Here the vertex is (1,24).

To find the x-intercepts we set y=0:








The vertex is at (1,24) and the intercepts are `x=1+-2sqrt(3)` so the answer is (d)


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Write the equation `y=-2(x-1)^2+24` in standard form.




The x coordinate of the vertex `x_v` of a parabola `y=ax^2+bx+c` is:


Substitute 4 for b and -2 for a.


Determine y(1)



Thus the vertex is at (1,24)

Determine the x intercepts by equating y to 0.


` ` Divide by -2 to simplify.


Use the quadratic formula to solve.


Substitute -2 for b, 1 for a and -11 for c.






Thus the x intercepts are `1+2sqrt3` and `1-2sqrt3`

Thus the answer is d)

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