Answer:
y + 16 = -1(x + 3)²
Explanation:
Looking at the graph, parabola vertex opens upwards with x intercepts as -5 and -1.
Thus, the line of symmetry will be;
x = (-5 + (-1))/2 = -3
Looking at the graph we can see that the vertex when traced to the x - coordinate will be 3 which is same with what we got.
Now, the general form of the equation will be;
y - h = a(x - k)²
where (k,h) is the vertex coordinate
Thus, k = -3
So;
y - h = a(x - (-3))²
>> y - h = a(x² + 6x + 9) =
>> y = ax² + 6ax + 9a + h
When, x = 0
y = 9a + h
From the graph, we can see that the y-intercept is y = -25
Thus;
9a + h = -25
From the graph, h which is the y-coordinate of the vertex = -16
Thus;
9a - 16 = - 25
9a = -25 + 16
9a = -9
a = -9/9
a = -1
Thus, the equation is;
y - (-16) = -1(x - (-3))²
>> y + 16 = -1(x + 3)²