Question

The most appropriate equation which represents the graph above is:

• A. $y=-x^4+6$
• B. $y=-(x^2+6)$
• C. $y=-x^2+6$
• D. $y=x^4+6$

Answer 1

The correct option is B $y=-(x^2+6)$

we know thet vertex form of parabola when vertex is (h,k) is

$Y=a{(x-h)}^2+k$

If $a<1$ , the graph of the parabola widens. This just means that the "U" shape of parabola stretches out sideways .

If $a>1$, the graph of the graph becomes narrower(The effect is the opposite of $a>1$).

As per graph the vertex of parabola (-6,0)then the equation of parabola is

$y=-{(x+0)}^2+(-6)$

$\Rightarrow y=-x^2-6$

$\Rightarrow y=-(x^2+6)$