A coordinate grid is mapped onto a video game screen, with the origin at the lower left corner. The game designer programs a turtle to move along a linear path that passes through the points (0, 0) and (10, 8).

The designer also programs a bird with a path that can be modeled by a quadratic function. The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8).

What are the values of the constants in the vertex form of the quadratic equation that models the bird's path?

h=
k=
a=

Since the vertex form of a parabola is y=a(x-h)^2+k with h and k being the vertex (the x and y values, respectively), we get a(x-0)^2+20=ax^2+20. Plugging (10, 8) in to find a, we get 8=a(10)^2+20=a*100+20. Subtracting 20 from both sides, we get -12=100*a. Next, we divide 100 from both sides to get a=-12/100. Since h=0 and k=20, we have your answer!

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MrRoyal MrRoyal · Answer 2 · 2021-10-19T17:30:31+02:00

The bird follows a parabolic path.

The values of h, k and a are: [tex]\mathbf{h = 0}[/tex] [tex]\mathbf{k = 20}[/tex] [tex]\mathbf{a = -0.12}[/tex]

The given parameters are:

[tex]\mathbf{Vertex = (0,20)}[/tex]

[tex]\mathbf{(x,y) = (10,8)}[/tex] --- a point on the path

The vertex of a quadratic function is represented as:

Vertex = (h,k)

So, by comparison:

[tex]\mathbf{h = 0}[/tex]

[tex]\mathbf{k = 20}[/tex]

The general equation of parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Substitute values for h and k

[tex]\mathbf{y = a(x - 0)^2 + 20}[/tex]

[tex]\mathbf{y = a(x)^2 + 20}[/tex]

[tex]\mathbf{y = ax^2 + 20}[/tex]

Substitute [tex]\mathbf{(x,y) = (10,8)}[/tex]

[tex]\mathbf{8 = a\times 10^2 + 20}[/tex]

[tex]\mathbf{8 = 100a + 20}[/tex]

Subtract 20 from both sides

[tex]\mathbf{-12 = 100a }[/tex]

Divide both sides by 100

[tex]\mathbf{a = -0.12}[/tex]

So, we have:

[tex]\mathbf{h = 0}[/tex]

[tex]\mathbf{k = 20}[/tex]

[tex]\mathbf{a = -0.12}[/tex]

Read more about equations of parabola at:

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