The correct option is
C Equation for the graph is 4x2+5![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1527905/original_123.PNG)
From the graph, we observe:
The y-axis is the line of symmetry of the graph, but y = 4 is parallel to the x-axis. So, it cannot be the line of symmetry for the given graph.
So, first option is incorrect.
If a graph of a quadratic function opens upwards, like the one given here, then its vertex is said to be the minimum or the lowest point of the graph.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1449561/original_2_1.png)
The lowest point on the graph is (0,5).
So, second option is incorrect.
Now, for the
equation of the graph, we see:
At x=0, y=4(0)2+5=5
At x=2, y=4(2)2+5=21
At x=3, y=4(3)2+5=41
At x=−2, y=4(−2)2+5=21
At x=−3, y=4(−3)2+5=41
It is in the form of y=4x2+5
Hence, we can say that equation
representing the given graph is 4x2+5.
So, third option is correct.
The slope of the graph does not look to be a straight line. It decreases, and then increases.
Hence, the given graph is not linear.
Also, the output is 5 when input is 0. The graph touches the y-axis at 5. So, the lowest value on the graph is 5 and not 0.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1449561/original_2_1.png)
So, last option is incorrect.