Answer:
[tex]g(x) = 8\cdot (x-3)^{2}-5[/tex]
Step-by-step explanation:
Given that parent function represents a parabola, the standard form with a vertex at (h,k) is now described:
[tex]y-k = C\cdot (x-h)^{2}[/tex]
[tex]y = C \cdot (x-h)^{2} + k[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Independent and dependent variables, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical component of the vertex, dimensionless.
[tex]C[/tex] - Vertex factor, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, there is an absolute maximum).
After reading the statement of the problem, the following conclusion are found:
1) New function must have an absolute minimum: [tex]C > 0[/tex]
2) Transformation to the right: [tex]h > 0[/tex].
3) Transformation downwards: [tex]k < 0[/tex]
Hence, the right choice must be [tex]g(x) = 8\cdot (x-3)^{2}-5[/tex].
