Shown in the graph
Explanation:
Using graph tools we can graph the function:
[tex]g(x)=4x^2-16[/tex]
which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:
[tex]Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:[/tex]
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]
Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it [tex]h(x)[/tex]) will be:
[tex]h(x)=4\left(x-9\right)^{2}-16-1 \\ \\ Simplifying: \\ \\ h(x)=4\left(x-9\right)^{2}-17[/tex]
This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:
[tex](0,-16)[/tex]
By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:
[tex]New \ vertex: \\ \\ (0+9,-16-1) \\ \\ (9,-17)[/tex]
Learn more:
Cubic function: https://brainly.com/question/13773618#
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