Answer:
f(x) = 2(x - 2)² - 1
Step-by-step explanation:
Given the vertex, (2, -1) and the point, (0, 7), we can plug these values into the vertex form of the quadratic function:
f(x) = a(x - h)² + h
where:
vertex = (h, k)
a = determines whether the graph opens up or down, and the wideness or narrowness of the parabola.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
We could substitute the given values into the vertex form, and solve for the value of "a":
f(x) = a(x - h)² + h
7 = a(0 - 2)² - 1
7 = a(-2)² - 1
7 = a(4) - 1
Add 1 to both sides:
7 + 1 = a(4) - 1 + 1
8 = 4a
Divide both sides by 4 to solve for a:
8/4 = 4a/4
2 = a
Since a = 2, and the vertex = (2, -1) then we could plug this value into the given function:
f(x) = 2(x - 2)² -1
Attached is a screenshot of the graph where it contains the given points.
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