The vertex form of the given quadratic equation is
.
According to the given question.
We have a quadratic equation
![4x^{2} -8x + 20 = 0](https://tex.z-dn.net/?f=4x%5E%7B2%7D%20-8x%20%2B%2020%20%3D%200)
Since, for the standard quadratic form is
, the vertex form of a quadratic equation is
where (h, k) is the vertex.
And h and k can be calculated as
h = -b/2a and y = k
So, for the given equation
the vertex (h, k) is given by
h = -(-8)/2(4) = 8/8 = 1 (X coordinate of vertex)
and,
![y =4x^{2} -8x+ 20](https://tex.z-dn.net/?f=y%20%3D4x%5E%7B2%7D%20-8x%2B%2020)
substitute x = 1 in the above equation for the value of k
Y = 4(1)(1) - 8(1) + 20
⇒ Y = 4 - 8 + 20
⇒ Y = -4 + 20
⇒ Y = 16
so, k = 16 (Y coordinate of vertex)
Now, substitute the value of a, k and h in
.
⇒ ![0 =4(x-1)^{2} + 16](https://tex.z-dn.net/?f=0%20%3D4%28x-1%29%5E%7B2%7D%20%2B%2016)
Therefore, the vertex form of the given quadratic equation is
.
Find out more information about vertex form of a quadratic equation here:
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