Find the quadratic function y=f(x) whose graph has a vertex (−3,3) and passes through the point (−6,0). What is the functi
on in standard form?
1 answer:
Answer:
f(x) = -1/3x² -2x
Step-by-step explanation:
For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...
y = a(x -h)² +k
For the given vertex, the vertex form function with scale factor "a" is ...
f(x) = a(x +3)² +3
If that goes through the point (-6, 0), then we have ...
f(-6) = a(-6 +3)² +3 = 0
9a = -3 . . . . . . . subtract 3
a = -1/3 . . . . . . . divide by 9
In standard form, the equation is ...
f(x) = (-1/3)x² -2x
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