Answer:
The quadratic function in vertex form is [tex]f(x)=(x+6)^2-10[/tex]
Step-by-step explanation:
Given equation of quadratic function [tex]f(x)=x^2+12x+26[/tex]
We have to write the given quadratic function in vertex form.
For a given quadratic function [tex]f(x)=ax^2+bx+c[/tex] can rewritten in standard form by completing the square.
The standard form of quadratic function [tex]f(x)=a(x-h)^2+k[/tex] , where (h,k) denotes the vertex of the equation.
If a is positive, the graph opens upward, and if a is negative, then it opens downward.
Consider the given function [tex]f(x)=x^2+12x+26[/tex]
Using algebraic identity [tex](a+b)^2=a^2+b^2+2ab[/tex]
We have a = x and 2ab = 12x ⇒ b = 6
Adding [tex]b^2[/tex] term to complete square and subtract so that the function remain same, we have,
[tex]f(x)=x^2+12x+36-36+26[/tex]
[tex]f(x)=(x+6)^2-10[/tex]
Which is in form of standard form of quadratic function.
Thus, The quadratic function in vertex form is [tex]f(x)=(x+6)^2-10[/tex]
