This graph represents Option D = [tex]-3(x+2)^{2} + 4[/tex]
As the given figure is a parabola, it will have quadratic equation because the general equation of parabola corresponds to [tex]x^{2} = 4ay[/tex] which has highest power of the variable equals to 2, thus its a quadratic equation.
The maximum value of a quadratic equation [tex]ax^{2} + b x +c[/tex] is at points
[tex](-b/2a, c-\frac{b^{2} }{4a} )[/tex]
By looking at the graph we can observe the point at which the graph has achieved maxima is (-2,4).
∴ ([tex]-b/2a = -2[/tex] , [tex]c-\frac{b^{2} }{4a} = 4[/tex]
The coefficient of [tex]x^2[/tex] should be negative the graph opens downwards.
∴ Option B and C are eliminated.
On putting x = -2 only option D yields 4.
Thus this graph represents Option D = [tex]-3(x+2)^{2} + 4[/tex]
Learn more about quadratic equation here :
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