The vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).
<h3>What is the Equation of a parabola?</h3>
The general equation of a parabola is given as,
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
As we want to write a function g(x) = 40x + 4x² in vertex form, and we know that the vertex form of a parabola, with vertex at (h,k) is written as,
Also, the algebraic identity is written as,
,
Therefore, can be written as
Further, we try to write the g(x) in the vertex form it can be written as,
Hence, the vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).
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