The vertex form of the quadratic equation, for the vertex points at which the parabola crosses its symmetry, is,
[tex]\rm f(x)=8[(x+\dfrac{1}{4})^2]-\dfrac{1}{2}[/tex]
Vertex form of the parabola is the equation form of the quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of the parabola is given as,
[tex]\rm y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The given quadratic equation in the problem is,
[tex]\rm f(x)=8x^2+4x[/tex]
To isolate the term, take out the common number 8 from the equation,
[tex]\rm f(x)=8(x^2+0.5x)[/tex]
Add and subtract 0.5/2 in the equation as;
[tex]\rm f(x)=8(x^2+0.5x+\dfrac{0.5}{2}-\dfrac{0.5}{2})\\\\f(x)=8(x^2+0.5x+\dfrac{1}{16}-\dfrac{1}{16})\\\\f(x)=8((x^+0.5x)^2-\dfrac{1}{16})\\\\f(x)=8[(x+\dfrac{1}{4})^2]-\dfrac{1}{2}[/tex]
The above equation is the vertex form of the given quadratic equation. Thus, option A is the correct option.
Learn more about the vertex form of the parabola here;
brainly.com/question/17987697
Answer:
simple answer for people that dont know its A
Step-by-step explanation:
