Shown in the graph
<h2>
Explanation:</h2>
Using graph tools we can graph the function:
![g(x)=4x^2-16](https://tex.z-dn.net/?f=g%28x%29%3D4x%5E2-16)
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:
![Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:](https://tex.z-dn.net/?f=Let%20%5C%20c%20%5C%20be%20%5C%20a%20%5C%20positive%20%5C%20real%20%5C%20number.%20%5C%20%5Cmathbf%7BVertical%20%5C%20and%20%5C%20horizontal%20%5C%20shifts%7D%20%5C%5C%20in%20%5C%20the%20%5C%20graph%20%5C%20of%20%5C%20y%3Df%28x%29%20%5C%20are%20%5C%20represented%20%5C%20as%20%5C%20follows%3A)
![\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)](https://tex.z-dn.net/?f=%5Cbullet%20%5C%20Vertical%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20%5Cmathbf%7Bupward%7D%3A%20%5C%5C%20h%28x%29%3Df%28x%29%2Bc%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Vertical%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20%5Cmathbf%7Bdownward%7D%3A%20%5C%5C%20h%28x%29%3Df%28x%29-c%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Horizontal%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20to%20%5C%20the%20%5C%20right%20%5C%20%5Cmathbf%7Bright%7D%3A%20%5C%5C%20h%28x%29%3Df%28x-c%29%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Horizontal%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20to%20%5C%20the%20%5C%20left%20%5C%20%5Cmathbf%7Bleft%7D%3A%20%5C%5C%20h%28x%29%3Df%28x%2Bc%29)
Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it
) will be:
![h(x)=4\left(x-9\right)^{2}-16-1 \\ \\ Simplifying: \\ \\ h(x)=4\left(x-9\right)^{2}-17](https://tex.z-dn.net/?f=h%28x%29%3D4%5Cleft%28x-9%5Cright%29%5E%7B2%7D-16-1%20%5C%5C%20%5C%5C%20Simplifying%3A%20%5C%5C%20%5C%5C%20h%28x%29%3D4%5Cleft%28x-9%5Cright%29%5E%7B2%7D-17)
This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:
![(0,-16)](https://tex.z-dn.net/?f=%280%2C-16%29)
By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:
![New \ vertex: \\ \\ (0+9,-16-1) \\ \\ (9,-17)](https://tex.z-dn.net/?f=New%20%5C%20vertex%3A%20%5C%5C%20%5C%5C%20%280%2B9%2C-16-1%29%20%5C%5C%20%5C%5C%20%289%2C-17%29)
<h2>
Learn more:</h2>
Cubic function: brainly.com/question/13773618#
#LearnWithBrainly
Answer:
=8
Step-by-step explanation:
Evaluate for x=y,y=x
8+5(x−x)
8+5(x−x)
Let's solve the inequality. Subtract 5 from both sides. The result will be
<span>x ≥ 5. This states, "x is equal to or greater than 5."
</span>
Plot 5 on the number line, using a dark solid dot. Then draw an arrow from that point to the right.
Top left, none
middle, many
top right, one
bottom left, none
if you extend the top and bottom left graphs, they won’t intercept. but if u extend the middle graph, they always intercept. and the top right graph only intercepts once