Question

what list of transformations correctly describes h(x)? h(x)=-7(x - 21)^2+15 vertical reflection vertical stretch of 7 horizontal shift left 21 vertical shift up 15 horizontal reflection vertical stretch of 7 horizontal shift right 21 vertical shift up 15 vertical reflection vertical stretch of 7 horizontal shift right 21 vertical shift up 15 vertical reflection vertical stretch of 7 horizontal shift right 21 vertical shift down 15

Explanation:

Step1: Analyze vertical reflection

The negative sign in front of the 7 in $h(x)= - 7(x - 21)^2+15$ reflects the graph of the parent - function $y = x^2$ vertically over the x - axis.

Step2: Analyze vertical stretch

The coefficient 7 in front of the $(x - 21)^2$ term vertically stretches the graph by a factor of 7.

Step3: Analyze horizontal shift

The $(x - 21)$ term indicates a horizontal shift. Since it is in the form $(x - a)$ with $a = 21$, the graph is shifted 21 units to the right.

Step4: Analyze vertical shift

The + 15 at the end of the function indicates a vertical shift of 15 units up.

Answer:

Vertical Reflection
Vertical Stretch of 7
Horizontal Shift Right 21
Vertical Shift Up 15