Question

The graph of which quadratic equation is shown below?

Answer 1

Well what kind of shape does it look like to you?

Answer 2

Or maybe does it look like some shape of a general function that you know but maybe just upside down?? :D

Answer 3

it's a parabola

Answer 4

clearly this is parabola.

as the curve cuts x-axis at -4 and 2, these are the two roots of the equation of the curve.so\[(x+4)(x-2)=0\]
since this curve has a maxima, its 2nd differentiation should be -ve. i.e; coefficient of \[x ^{2}\] should be -ve.
or
since this function approaches to -ve infinity as x tends to -ve or +ve infinity, coefficient of x^2 should be -ve.
so multiply above equation by -1.
we get:
\[-x ^{2} -2x + 8 = 0\]
which is the equation of the curve in the given fig.