The equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].
What is the general equation of parabola?
The general equation of parabola is [tex]y = a(x-h)^{2} + k[/tex].
Where,
(h, k) are the vertices of the parabola.
According to the given question.
We have two graph.
The blue and red graph both represents the equation of downward parabola.
Since, blue graph represents the equation of downward parabola.
Whose equation is given
[tex]G(x) = 5 - x^{2}..(i)[/tex]
The general equation of a parabola is [tex]y = a(x-h)^{2} + k..(ii)[/tex]
Where, (h, k) are the vertices of the parabola.
Compare the equation (i) with (ii)
We get
(h, k) = (0, 5) and a = -1.
Now, the red graph which also represents the downward parabola whose vertices are (0, 2)
Therefore, the equation red graph is given by
[tex]F(x) = a(x-0)^{2} + 2[/tex]
⇒ [tex]F(x) = -1(x-0)^{2} + 2[/tex]
⇒ [tex]F(x) = 2 - x^{2}[/tex]
Hence, the equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].
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