Question

Need help with Math (Quadratic)

Answer 1

Answer:

  f(x) = 2(x -3)² +5   or   f(x) = 2x² -12x +23

Step-by-step 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