Answer:
7) [tex]x \to x - 3[/tex].
8) [tex]y \to y + 2[/tex]
9) The entire quadratic equation did not get reflected.
Step-by-step explanation:
7) A horizontal translation to the right is of the form:
[tex]x \to x - a[/tex]
Let [tex]y = -(x-3)^{2} + 2[/tex], then the horizontal translation is represented by [tex]x \to x - 3[/tex].
8) A vertical translation upwards is of the form:
[tex]y \to y + a[/tex]
Let [tex]y = -(x-3)^{2} + 2[/tex] , then the vertical translation is represented by:
[tex]y \to y + 2[/tex]
9) The only component of the quadratic equation that was reflected was the part [tex](x-3) ^{2}[/tex] along the x-axis. We can create the entire function by applying the following steps:
(i) [tex]f(x) = x^{2}[/tex] (Original function)
(ii) [tex]f(x) = (x-3)^{2}[/tex] (Horizontal translation)
(iii) [tex]f(x) = - (x-3)^{2}[/tex] (Reflection)
(iv) [tex]f(x) = -(x-3)^{2} + 2[/tex] (Vertical translation)
The entire quadratic equation did not get reflected.
