Question

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 1

Answer:

(2,4)

Step-by-step explanation:

The given function is

$y=5x^{2} -20x+24$

Where $a=5$, $b=-20$ and $c=24$.

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

$h=-\frac{-20}{2(5)}=\frac{20}{10}=2$

Then, $k=f(2)=5(2)^{2} -20(2)+24=5(4)-40+24=20-40+24=4$

So, the vertex is at $V(2,4)$.

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).