Respuesta :
The function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
What is the vertex form of parabola?
Vertex form of parabola is the equation form of 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 parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The first three steps in writing the function in vertex form are shown.
[tex]f(x) = 40x +5x^2[/tex]
Write the function in standard form.
[tex]f(x) = 5x^2+ 40x[/tex]
Factor out of the first two terms by taking out the common number 5 from the equation,
[tex]f(x) = 5(x^2 +8x)[/tex]
Form a perfect square trinomial with (8/2)² = 16,
[tex]f(x) = 5(x^2 +8x+ 16) - 5(16)\\f(x) = 5(x+4)^2 - 80[/tex]
Hence, the function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
Learn more about the vertex form of the parabola here;
https://brainly.com/question/17987697
