Respuesta :

taskmasters
The equation is a quadratic equation, and it represents a parabola, opening upward. The standard form of this parabola is (x – h)^2 = 4a (y – k) f(x) = y = 8( x^2 + (1/2)x) y + ½ = 8( x^2 + (1/2)x + 1/16) (1/8)(y + ½) = (x + ¼)^2 Vertex is at (-1/4, -1/2)
calculista

we have

[tex] f(x)=8x^{2} +4x [/tex]


Let

[tex] y=f(x) [/tex]


[tex] y=8x^{2} +4x [/tex]


Factor the leading coefficient

[tex] y=8(x^{2} +0.5x) [/tex]


Complete the square. Remember to balance the equation by adding the same constants to each side

[tex] y+0.5=8(x^{2} +0.5x+0.0625) [/tex]


Rewrite as perfect squares

[tex] y+0.5=8(x+0.25)^{2} [/tex]

[tex] f(x)=8(x+0.25)^{2}-0.5 [/tex]------> equation in vertex form


therefore


the answer is

[tex] f(x)=8(x+0.25)^{2}-0.5 [/tex]