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# Finding the vertex help thanks!

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Find the vertex of the graph of the equation y=-2x^2+8x-15.

Mar 20, 2021

#1
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Complete the square on y = -2x^2 + 8x -15.

Then y = -2(x - 4)^2 + 17, so the vertex is (4,17).

Mar 20, 2021
#3
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x coordinate =   - b/2a =  -  8/-4 =  2

sub into equation to find y   coordinate     -2(2^2) + 8 (2) - 15 = -7                (2, -7)

ElectricPavlov  Mar 20, 2021
#2
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y  =  -2x2 + 8x - 15

Move the '-15' term to the other side by adding 15 to both sides:

y + 15  =  -2x2 + 8x

Factor out the '-2' term:

y + 15  =  -2(x2 - 4x)

Complete the square of x2 - 4x     --->     x2 - 4x + 4

Notice that the '4' will be on the inside of the factor, so really, it is a '-8':

y = 15 - 8  =  -2(x2 - 4x + 4)

Finishing:

y + 7  =  -2(x - 2)2

The vertex occurs at (2, -7)

Mar 20, 2021
#4
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We  have  the form   y = ax^2  + bx  + c

The  x coordinate of the  vertex  occurs  at  - b / (2a)  =  -8/ ( 2 *-2)  =  -8 / -4  = 2

To find the y coordinate...put x  back into  the function

y= -2(2)^2  + 8(2)  -15  =    -8  + 16  - 15 =  -7   Mar 20, 2021