Answer :
Vertex form
[tex]a\left\{(x+\frac{b}{2a})^2-(\frac{b}{2a})^2\right\}+c[/tex]
Step-by-step explanation:
We are given than a quadratic function in standard form
[tex]ax^2+bx+c[/tex]
We have to explain steps which is necessary for converting quadratic x function in standard form to vertex form
We are explaining steps for converting a quadratic function into vertex form with the help of example
Suppose we have a quadratic function
[tex]2x^2+x-1[/tex]
Taking 2 common from the given function the we get
[tex]2(x^2+\frac{x}{2})-1[/tex]
Now, we convert the equation of the form [tex](a+b)^2 or (a-b)^2[/tex]
[tex]2\left \{(x)^2+2\times x\times\frac{1}{4}+\frac{1}{16}-\frac{1}{16}\right\}-1[/tex]
[tex]2\left\{(x+\frac{1}{4})^2-\frac{1}{16}\right\}-1[/tex]
[tex]2\left\{(x+\frac{1}{4})^2-(\frac{1}{4})^2\right\}-1[/tex]
Vertex form=[tex]2\left\{(x+\frac{1}{4})^2-(\frac{1}{4})^2\right\}-1[/tex]
Hence , the vertex form=[tex]a\left\{(x+\frac{b}{2a})^2-(\frac{b}{2a})^2\right\}+c[/tex]
