Question

Finding the Vertex

What is the vertex of the quadratic function f(x) = (x – 6)(x + 2)?

Answer 1

The answer to this is ( x,y)=(2,-16)

Answer 2

The vertex of the quadratic function is (2 , -16)

What is a function?

An expression which defines the relationship between two variables (one independent and one dependent variable).

What is dependent and independent variable?

The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes with the change of independent variable.

What is a quadratic function?

A function whose highest degree is 2 is called a quadratic function.

What is a parabolic function?

Quadratic function is also called the parabolic function since the graph of the function will be a parabola.

How to find the vertex of the quadratic expression?

• We know that the standard equation of parabola is

                                 $(y-\beta )^{2} =4a(x-\alpha )$.

• Here, the vertex of the parabola is ($\alpha ,\beta$).
• Now, we need to make the given function in the form of $(y-\beta )^{2} =4a(x-\alpha )$

f(x) = (x – 6)(x + 2)

      =   $x^{2} -4x-12$

      =   $x^{2} -4x+4-4-12$                      

      =  $(x-2)^{2} -16$

⇒ y =  $(x-2)^{2} -16$

⇒ y + 16 = $(x - 2)^{2}$

We can write the equation in the form.

⇒ (y + 16) = 4($\frac{1}{4}$) $(x - 2)^{2}$

• Comparing this equation with the standard equation $(y-\beta )^{2} =4a(x-\alpha )$   , we get,

α = 2 and β = -16

∴ These are the coordinates of vertex of the quadratic function.

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