Chapter 7.5, Problem 8OE

To determine

To match given equation to one of the graphs given.

Explanation of Solution

Given information :

Given equation $y-1=-\frac{1}{3}{\left(x-2\right)}^2$

We know that the graph of the equation $y-k=a{\left(x-h\right)}^2$ the parabola formed opens upwards when $a>0$ and downwards when $a<0$ . Higher the values of $a$ , narrower the parabola will be. Further if $h>0$ then the graph will slide to its right whereas it will shift on left side if the value of $h<0$ .

When $k>0$ the graph slides upwards and when $k<0$ then graph slides downwards.

When we compare the equation with standard equation we get $a=-\frac{1}{3},h=2$

Since $a<0$ graph will open downwards further it shifts 2 units to the right.

Also the value of $k=1$ therefore there will be 1 unit upward shift of parabola.

Answer for given equation is,