Question

which equation best matches the graph shown below?
answer
$y = 0.4(x + 2)^2 - 6$
$y = 0.4(x + 2)^2 + 6$
$y = 0.4(x - 2)^2 + 6$
$y = 0.4(x - 2)^2 - 6$

Explanation:

Step1: Identify vertex form

The vertex form of a parabola is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex.

Step2: Locate the vertex

From the graph, the vertex is at $(-2, -6)$, so $h=-2$, $k=-6$.

Step3: Substitute vertex into form

Substitute $h$ and $k$: $y=a(x+2)^2-6$.

Step4: Verify leading coefficient

The parabola opens upward, so $a>0$. The given $a=0.4$ matches, and the vertex coordinates confirm the equation.

Answer:

$y=0.4(x+2)^2-6$