Answer:
y = -5/8(x -8)²
Step-by-step explanation:
You want the function of the form y = a(x -h)² that passes through the points (12, -10) and (8, 0).
Vertex form
The vertex form of the equation of a quadratic is ...
y = a(x -h)² +k . . . . . . quadratic with vertex (h, k)
Comparing this to the given equation, we see that k=0. This means the point (8, 0) is the vertex and h = 8.
Scale factor
The value of 'a' can be found using the other point.
(x, y) = (12, -10)
-10 = a(12 -8)²
-10 = 16a
-5/8 = a . . . . . . divide by 16 and reduce the fraction
The quadratic function is y = -5/8(x -8)².
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Additional comment
The equation can also be found using technology to do a quadratic regression with the constraint that the vertex is on the x-axis.
