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Complete the square to re-write the quadratic function in vertex form:Answer:
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Q. Complete the square to re-write the quadratic function in vertex form:Answer:
- Identify vertex form: Identify the vertex form of a parabola.The vertex form of a parabola is given by , where is the vertex of the parabola.
- Begin with quadratic function: Begin with the given quadratic function.We have the quadratic function .
- Separate constant term: Separate the constant term from the -terms.To complete the square, we need to isolate the -terms. So we write the function as .
- Find completing square value: Find the value needed to complete the square.To complete the square for the expression , we take half of the coefficient of , which is , and then square it, which gives us .
- Add/subtract value: Add and subtract the value found inside the parentheses.We add and subtract the value inside the parentheses to maintain the equality: .
- Rewrite with perfect trinomial: Rewrite the equation with a perfect square trinomial.Now we have a perfect square trinomial inside the parentheses: .
- Simplify equation: Simplify the equation.Combine the constants outside the parentheses: .
