The vertex form of a quadratic equation is [tex]y=a(x-h)^2+k[/tex] and the vertex is (h, k) converted from the standard form [tex]y=ax^2+bx+c[/tex].
What is the standard form of a quadratic function?
The standard form of a quadratic function is [tex]y=ax^2+bx+c[/tex].
The equation whose variable's highest degree is 2 is said to be a quadratic equation.
Steps to convert standard form to vertex form:
The standard form is
[tex]y=ax^2+bx+c[/tex]
Step 1: taking a common from the terms
⇒ [tex]y=a(x^2+\frac{b}{a} x)+c[/tex]
Step 2: Factorization
[tex]y=a(x^2+\frac{b}{a} x+(\frac{b}{2a})^{2} -(\frac{b}{2a})^{2}) +c[/tex]
[tex]y=a(x+\frac{b}{2a} )^2+c-\frac{b^2}{4a}[/tex]
Step 3: Writing in the vertex form
[tex]y=a(x-(-\frac{b}{2a}) )^2+c-\frac{b^2}{4a}[/tex]
Where h = [tex]-\frac{b}{2a}[/tex] and k = [tex]c-\frac{b^2}{4a}[/tex]
So, the quadratic function's vertex form is [tex]y=a(x-(-\frac{b}{2a}) )^2+c-\frac{b^2}{4a}[/tex].
Learn more about the vertex form of quadratic functions here:
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