How do I find the focus of the parabola represented by #y=2x^2-8x+9#?

1 Answer
Oct 19, 2015

Answer:

#(2,-135/8)#

Explanation:

First, we must convert the equation into the vertex-form:

#color(white)([1]XX)y=a(x-h)^2+k#

Solution:

#[1]color(white)(XX)y=2x^2-8x-9#

#[2]color(white)(XX)y+9=2x^2-8x#

#[3]color(white)(XX)y+9=2(x^2-4x)#

#[4]color(white)(XX)y+9+2(4)=2(x^2-4x)+2(4)#

#[5]color(white)(XX)y+9+8=2(x^2-4x+4)#

#[6]color(white)(XX)y+17=2(x-2)^2#

#[7]color(white)(XX)color(red)(y=2(x-2)^2-17)#

Now that we have the equation in vertex form, we can easily get the focus:

Focus: #color(white)([1]X)(h, k + 1/(4a))#

Solution:

#[1]color(white)(XX)(h, k+1/(4a))#

#[2]color(white)(XX)((2), (-17)+1/(4(2)))#

#[3]color(white)(XX)(2, -17+1/8)#

#[4]color(white)(XX)color(red)((2","-135/8))#