Question

Bonus: 2 points for vertex form or standard form, 5 points for both

Write the equation for the quadratic function the has a vertex at (3,-5) and includes
the point (-1,11)

Answer 1

9514 1404 393

Answer:

• y = (x -3)² -5
• y = x² -6x +4

Explanation:

The vertex form of the quadratic equation is ...

y = a(x -h)² +k . . . . . . . . . vertex (h, k); vertical scale factor 'a'

Given the vertex, we can find the scale factor by substituting the given point values:

11 = a(-1 -3)² -5

11 = 16a -5

a = (11 +5)/16 = 1

So, the vertex form equation is ...

y = (x -3)² -5 . . . . . vertex form

Expanding this gives the standard form.

y = x² -6x +9 -5

y = x² -6x +4 . . . . . standard form