Two springs look alike but have different spring constants. how could you determine which one has the greater spring constant?

As we know that spring force on a system of spring is given as

here we know that

k = spring constant

x = deformation in the spring

F = spring force

So here we know that from above formula we have

so on applying same force if two springs have different deformations then the spring with small amount of deformation the value of spring constant will be more

so here in order to find the spring with greater spring constant we will suspend same mass in both springs so there will be equal force on both the springs.

Now the spring with lesser deformation will have more spring constant

Remember that the vertex form of a parabola is where is the vertex of the parabola.

Now, to find the vertex of the parabola, we are going to use the vertex formula:

For a quadratic of the form , the vertex is given by:

in other words, we find by evaluating the function at

We know form our quadratic that and , so let's use our formula to find :

Now we can evaluate our function at to find :

Now, we can rewrite our parabola in vertex form:

, , and

We can conclude that the correct answer is: y = 6(x + 1)2 – 16