To write the equation of the quadratic function in vertex form, we need to find the vertex coordinates (h, k). The vertex is the point on the graph where the function reaches its maximum or minimum.
Looking at the graph provided, we can see that the vertex of the quadratic function is at the point (4, -12).
Now, we have the vertex coordinates (h, k) = (4, -12).
Using the vertex form of a quadratic function, y = a(x-h)^2 + k, where (h, k) is the vertex, we can substitute the values of h and k into the equation:
y = a(x-4)^2 - 12
Now, we need to find the value of a, which is the coefficient of the squared term.
To determine a, we can use the point (0, 0) on the graph.
Substituting x = 0 and y = 0 into the equation, we get:
0 = a(0-4)^2 - 12
0 = a(-4)^2 - 12
0 = 16a - 12
12 = 16a
a = 12/16
a = 3/4
Substituting this value of a back into the equation, we get:
y = (3/4)(x-4)^2 - 12
Therefore, the equation of the quadratic function in vertex form is y = (3/4)(x-4)^2 - 12.
Use the graph to write the equation of the quadratic function in vertex form. (1 point) y=−12 (x− )2+
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