Question

Find the quadratic function y=​f(x) whose graph has a vertex ​(−3​,3​) and passes through the point ​(−6​,0). What is the function in standard form?

Answer 1

Answer:

  f(x) = -1/3x² -2x

Step-by-step explanation:

For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...

  y = a(x -h)² +k

For the given vertex, the vertex form function with scale factor "a" is ...

  f(x) = a(x +3)² +3

If that goes through the point (-6, 0), then we have ...

  f(-6) = a(-6 +3)² +3 = 0

  9a = -3 . . . . . . . subtract 3

  a = -1/3 . . . . . . . divide by 9

In standard form, the equation is ...

  f(x) = (-1/3)x² -2x