ANSWER:
1a)
*A reflection across the x-axis
*A vertical compression
*A horizontal translation 3 units left
*A vertical translation up 5 units
1b)
*A reflection across the x-axis
*A vertical stretch
*A horizontal translation 2 units right
*A vertical translation down 11 units
EXPLANATION:
Given:
[tex]\begin{gathered} f(x)=-\frac{1}{2}(x+3)^2+5 \\ h(x)=-3(x-2)^2-11 \end{gathered}[/tex]To:
Describe the transformation effects from the parent graph g(x) = x^2
Recall that a quadratic function in vertex form;
[tex]f(x)=a(x-h)^2+k[/tex]where;
a > 1 represents a vertical stretch
0 < a < 1 represents a vertical compression
-h represents horizontal translation right h units
+h represents horizontal translation left h units
k represents vertical translation up k units
-k represents vertical translation down k units
-a represents a reflection across the x-axis
1(a) Comparing the below-given function with the vertex function, the transformations are as listed below;
[tex]f(x)=-\frac{1}{2}(x+3)^2+5[/tex]*A reflection across the x-axis
*A vertical compression
*A horizontal translation 3 units left
*A vertical translation up 5 units
1(b) Comparing the below-given function with the vertex function, the transformations are as listed below;
[tex]h(x)=-3(x-2)^{2}-11[/tex]*A reflection across the x-axis
*A vertical stretch
*A horizontal translation 2 units right
*A vertical translation down 11 units
