Respuesta :
The specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]
What is vertex form of a quadratic equation?
If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
What is a perfect square polynomial?
If a polynomial p(x) can be written as:
[tex]p(x) = [f(x)]^2[/tex]
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial
For the considered case, the polynomial specified is;
[tex]g(x) = 40x + 4x^2[/tex]
- Case 1: Converting to vertex form
[tex]g(x) = 40x + 4x^2\\g(x) = 4(x^2 + 10) = 4(x^2 + 10 + 25 -25)\\g(x) = 4(x^2 + 10 + 25) - 100 = 4(x+5)^2 - 100\\[/tex]
Thus, the vertex form of the considered polynomial is [tex]g(x) = 4(x+5)^2 - 100[/tex]
- Case 2: Converting to standard form
Standard form of a quadratic polynomial is [tex]ax^2 + bx + c[/tex]
Thus, we get: the considered polynomial in standard form as:
[tex]g(x) = 4x^2 +40x[/tex]
- Case 3: Factoring the first two terms of polynomial
[tex]g(x) = 40x + 4x^2 \\g(x) = 4x(10 + x)[/tex]
- Case 4: Forming a perfect square trinomial
The considered polynomial has only two terms, therefore, its not a trinomial.
Thus, the specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]
Learn more about vertex form of a quadratic equation here:
https://brainly.com/question/9912128
Answer:
g(x)=4(x+5)^2-100
Step-by-step explanation:
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