Write the equation of a parabola that has vertex (2.5, 2.75) and passes throught the point (1,5).

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]

Read more about parabolas at:

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