Answer:
f(x) = 2(x -3)² +5 or f(x) = 2x² -12x +23
Explanation:
The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.
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vertex form
The vertex form equation for a parabola is ...
f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'
equation
For vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...
f(x) = 2(x -3)² +5 . . . . . vertex form equation
Expanded to standard form, this is ...
f(x) = 2(x² -6x +9) +5
f(x) = 2x² -12x +23 . . . . . standard form equation