What is Vertex Form?

Vertex form is an equation of the form y=a(x-h)^2+k, where a, h and k are the parameters, and x and y are independent and dependent variables (of the equation). This form is often used in the fields of mathematics and physics to denote the equation of a parabola, and it is known as the vertex form because h and k denote the coordinates of the “vertex,” or the highest (or lowest) point of the parabola.

Applications of Vertex Form

Vertex form is commonly used in mathematics and other scientific fields when dealing with parabolic equations. For example, say we want to determine the optimal outlook point of a mountain peak. We can use the vertex form expression y=a(x-h)^2+k to calculate the maximum y-coordinate of the mountain peak (k) and the point where the peak can be found (h). Additionally, vertex form equations can be used to calculate the maximum or minimum of a given equation by taking the derivative, setting it equal to zero, and then solving the equation.

Example of Vertex Form

Let’s look at the following example:

y=4x^2-6x-5

To convert this equation into vertex form, we have to identify the parameters a, h, and k. In this case, a=4, h=-3 and k=-5. Now that we know the parameters, we can substitute them into the vertex form equation to create the following vertex form equation:

y=4(x-(-3))^2+(-5)

y=4(x+3)^2-5

As you can see, this is the same equation as our original example, except this time written in vertex form.

Conclusion

To summarize, vertex form is a type of equation used to express the equation of a parabola, with h and k denoting the coordinates of the vertex, or the highest or lowest point of the parabola. This form of equation is commonly used to determine the maximum or minimum of a given function, or to calculate the peak of a mountain or other physical object.