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A quadratic equation can be written in the form =(−ℎ)2+ y = a ( x - h ) + k , where (h, k) is the vertex of the parabola. This form can be used to determine the minimum y-value of the related function. Which is the minimum y-value of =52−20+24 y = 5 x 2 - 20 x + 24 ?

Answer :

Answer:

(2,4)

Step-by-step explanation:

The given function is

[tex]y=5x^{2} -20x+24[/tex]

Where [tex]a=5[/tex], [tex]b=-20[/tex] and [tex]c=24[/tex].

The vertex is at [tex](h,k)[/tex], which is defined as [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex]. So, replacing values, we have

[tex]h=-\frac{-20}{2(5)}=\frac{20}{10}=2[/tex]

Then, [tex]k=f(2)=5(2)^{2} -20(2)+24=5(4)-40+24=20-40+24=4[/tex]

So, the vertex is at [tex]V(2,4)[/tex].

Remember that the minium or maximum value of a quadratic function is defined by its vertex. In this case, it represents a minimum at (2,4).

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