Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).
1 answer:
Answer:
f(x) = 9(x -1/3)^2 -3
Step-by-step explanation:
In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...
y = a(x -h)^2 +k
To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":
1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given
1 = (4/9)a -3 . . . . simplify
4 = (4/9)a . . . . . . add 3
9 = a . . . . . . . . . . multiply by 9/4
The quadratic function you desire is ...
f(x) = 9(x -1/3)^2 -3
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