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

1 Answer
Oct 19, 2015

(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))