Write the equation of the parabola in vertex form with vertex at (2,-5) and y intercept at -17.

y = -3(x -2)² -5

The equation of a parabola with vertex (h, k) is given by ...

... y = a(x -h)² +k . . . . . . . for some vertical scale factor "a".

We can find the value of "a" by substituting the coordinates of a point that is not the vertex. Here, that point is the y-intercept: (0, -17).

... y = a(x -2)² -5 . . . . . initial form of the equation for the parabola

... -17 = a(-2)² -5 . . . . . substitute y-intercept values

... -12 = 4a . . . . . . . . . . add 5, simplify

... -12/4 = a = -3

The desired equation is ... y = -3(x -2)² -5.

55

step-by-step explanation:

b.an increase in a causes b to decrease