Write a function in any form that would match the graph shown below.

y + 16 = -1(x + 3)²

Step-by-step 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

answer:

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step-by-step explanation:

step-by-step explanation:

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