Question

Observe the graph:
Select the correct statement(s) about the graph from the following options.

• A. y = 4 is the line of symmetry for the graph
• B. The vertex of the graph is (4,4)
• C. $\text{Equation for the graph is}4x^2+5$
• D. 0 is the smallest value on the graph and it is a linear graph

Answer 1

The correct option is C $\text{Equation for the graph is}4x^2+5$


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.


The lowest point on the graph is (0,5).

So, second option is incorrect.

Now, for the equation of the graph, we see:
$Atx=0,y=4(0{)}^2+5=5$

$Atx=2,y=4(2{)}^2+5=21$

$Atx=3,y=4(3{)}^2+5=41$

$Atx=-2,y=4(-2{)}^2+5=21$

$Atx=-3,y=4(-3{)}^2+5=41$

$\text{It is in the form of}y=4x^2+5$

$\text{Hence, we can say that equation}$
$\text{representing the given graph is}4x^2+5$.

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.


So, last option is incorrect.