ANSWER
See explanation
EXPLANATION
The standard form of a quadratic equation is:
[tex]y = a {x}^{2} + bx + c[/tex]
To convert this function to standard form, you follow the steps below:
- Factor 'a' from the variable terms
- Add and subtract the square of half the coefficient of x.
- Factor the perfect squares
- Simplify the constant terms to get the vertex form as
- [tex]y = a {(x - h)}^{2} + k[/tex]
For example:
Given the standard form:
[tex]y = 2 {x}^{2} + 12x + 10[/tex]
Factor 2 from the variable terms
[tex]y = 2 {(x}^{2} + 6x) + 10[/tex]
Add and subtract the square of 3.
[tex]y = 2 {(x}^{2} + 6x + 9 - 9) + 10[/tex]
[tex]y = 2 {(x}^{2} + 6x + 9) + 2( - 9) + 10[/tex]
Factor the perfect square an simplify
[tex]y = 2 ({x + 3)}^{2} - 8[/tex]
This is the vertex form
