Answer:
- vertex: (3, -7)
- point: (4, -5)
Explanation:
You want the vertex and another point on the parabola f(x) = 2x² -12x +11.
Vertex
The equation can be put into vertex form as follows:
f(x) = 2(x² -6x) +11 . . . . . . . factor the leading coefficient from the variable terms
f(x) = 2(x² -6x +9) +11 -2(9) . . . . add (6/2)² = 9 inside parentheses, subtract the same amount outside
f(x) = 2(x -3)² -7 . . . . . . . . simplify to vertex form
Comparing this to the vertex form equation ...
f(x) = a(x -h)² +k
we see that a=2, h=3, k=-7.
The vertex is (h, k) = (3, -7). This is one point on the parabola.
A second point
We can use a value for x that is near the value of h to obtain another point on the parabola without much work. Using x = 4, we have ...
f(4) = 2(4 -3)² -7 = 2(1) -7 = -5
Another point is (x, y) = (4, -5).
You can plot the vertex (3, -7) and the point (4, -5) to obtain your graph of the parabola using the parabola tool.
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Additional comment
The points and the parabola are shown in the attached graph.
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