Answer:
y = (x - 2.5)^2 + 2.75
Explanation:
y = a(x - h)^2 + k - Vertex form
y = a(x - 2.5)^2 + 2.75 - Replacing h with 2.5 and k with 2.75
5 = a(1 - 2.5)^2 + 2.75 - Replacing x with 1 and y with 5
5 = 2.25a + 2.75 - Doing (1 - 2.5)^2 = 2.25 times a = 2.25a
2.25 = 2.25a - Subtracting 2.75 on both sides
a = 1
y = 1(x - 2.5)^2 + 2.75 - Replacing a with 1
So the equation of a parabola is y = (x - 2.5)^2 + 2.75
The vertex of a parabola is the minimum or the maximum point of the parabola
The equation of the parabola is [tex]\mathbf{y = a(x -1)^2 + 5}[/tex]
The given parameters are:
[tex]\mathbf{(x,y) = (2.5,2.75)}[/tex] --- point
[tex]\mathbf{(h,k) = (1,5)}[/tex] -- vertex
A parabola is represented as:
[tex]\mathbf{y = a(x -h)^2 + k}[/tex]
Substitute the given values in the above formula
[tex]\mathbf{2.75 = a(2.5 -1)^2 + 5}[/tex]
[tex]\mathbf{2.75 = a(1.5)^2 + 5}[/tex]
[tex]\mathbf{2.75 = 2.25a + 5}[/tex]
Subtract 5 from both sides
[tex]\mathbf{2.25a =-2.25}[/tex]
Divide both sides by 2.25
[tex]\mathbf{a =-1}[/tex]
Substitute [tex]\mathbf{a =-1}[/tex] and [tex]\mathbf{(h,k) = (1,5)}[/tex] in [tex]\mathbf{y = a(x -h)^2 + k}[/tex]
[tex]\mathbf{y = a(x -1)^2 + 5}[/tex]
Hence, the equation of the parabola is [tex]\mathbf{y = a(x -1)^2 + 5}[/tex]
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