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)

<h3>What is a perfect square polynomial?</h3>

If a polynomial p(x) can be written as:

$p(x) = [f(x)]^2$

where f(x) is also a polynomial, then p(x) is called as perfect square polynomial

For the considered case, the polynomial specified is;

$g(x) = 40x + 4x^2$

Case 1: Converting to vertex form

$g(x) = 40x + 4x^2\\g(x) = 4(x^2 + 10) = 4(x^2 + 10 + 25 -25)\\g(x) = 4(x^2 + 10 + 25) - 100 = 4(x+5)^2 - 100\\$

Thus, the vertex form of the considered polynomial is $g(x) = 4(x+5)^2 - 100$

Case 2: Converting to standard form

Standard form of a quadratic polynomial is $ax^2 + bx + c$

Thus, we get: the considered polynomial in standard form as:

$g(x) = 4x^2 +40x$

Case 3: Factoring the first two terms of polynomial

$g(x) = 40x + 4x^2 \\g(x) = 4x(10 + x)$

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 $g(x) = 4(x+5)^2 - 100$

Learn more about vertex form of a quadratic equation here:

brainly.com/question/9912128

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