Question

which function does this graph represent
A. f(x) = 3(x + 1)^2 + 2
B. f(x) = -3(x + 1)^2 + 2
C. f(x) = -3(x + 1)^2 - 2
D. f(x) = 3(x - 1)^2 + 2​

Answer 1

The equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.

What is parabola?

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Here, general equation of parabola in downward direction is

(y-y₁) = -4a(x-x₁)²

vertex of parabola (-1, 2)

(y-2) = -4a(x-(-1))²

(y - 2) = -4a(x + 1)²

put the value of x = 0 and y = -1

so we get, a = 3/4

put in equation of parabola

( y - 2 ) = -3 ( x + 1 ) ²

y = -3 (x + 1)² + 2

f(x) = -3 (x + 1)² + 2

Thus, the equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.

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