Question

What function does this graph represent? f(x) 6 -4 -2 = 6- 4 2- A -6 lo 2 OA. f(x) = -3(x - 2)² + 4 OB. f(x) 3(x + 2)² + 4 Oc. f(x) = 3(x - 2)² + 4 OD. f(x) = -3(x + 2)² + 4​

Answer 1

This graph represents Option D = $-3(x+2)^{2} + 4$

As the given figure is a parabola, it will have quadratic equation because the general equation of parabola corresponds  to $x^{2} = 4ay$ which has highest power of the variable equals to 2, thus its a quadratic equation.

The maximum value of a quadratic equation $ax^{2} + b x +c$  is at points

$(-b/2a, c-\frac{b^{2} }{4a} )$

By looking at the graph we can observe the point at which the graph has achieved maxima is (-2,4).

∴ ($-b/2a = -2$ , $c-\frac{b^{2} }{4a} = 4$

The coefficient of $x^2$ 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 = $-3(x+2)^{2} + 4$

Learn more about quadratic equation here :

brainly.com/question/17177510

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