Answer :
The vertex of the parabola is = (4, 2)
What is Vertex?
A vertex, which is a unique point on a mathematical object, is typically where two or more lines or edges come together. The shapes that contain vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are also called nodes.
Given,
y = 2x² - 16x +34
can be made simpler by subtracting 2 from each of the three terms on the right side.
y = 2( x² - 8x + 17)
Here, we must "close the square."
We square this value by taking the half of the coefficient of x, which is -4. (which yields 16).
Focusing on x² - 8x + 17, we add 16, and then subtract 16, obtaining:
= x² - 8x + 16 - 16 + 17, or (x - 4)² + 1
Now return to the original function
y = 2(x² - 8x + 17).
Replace x² - 8x + 17 with [x - 4]² + 1
We get ,y = 2(x² - 8x + 17)
= 2( [x - 4]² + 1 )
By contrast, we can see that h = 4 and k = 2 in this equation, which has the form y = a(x - h)2 + k. This parabola's vertex is located at (4, 2).
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