Question

Convert y = 3x^2+ 60x - 150 to vertex form by completing the square. Choose thecorrect equation.a)y = 3(x + 10)2 - 450b) yy = 3(x + 10)2 + 250c) y = 3(x + 10)2 - 250d) y = 3(x + 10)2 - 50

Answer 1

We have the quadratic equation:

$y=3x^2+60x-150$

And want to write in the vertex form by completing the square, so we take the coefficient of squared x as a factor:

$\begin{gathered} y=3x^2+60x-150 \\ y=3(x^2+20x-50) \end{gathered}$

Take the coefficient of x and divided by 2 and the calculate the square, and add and substract the result into the parenthesys, so:

$\begin{gathered} y=3(x^2+20x-50+(\frac{20}{2})^2-(\frac{20}{2})^2) \\ y=3(x^2+20x+100-50-100) \\ y=3(x^2+20x+100-150) \\ y=3(x^2+20x+100)-3\cdot150 \\ y=3(x^2+20x+100)-450 \end{gathered}$

Now, write the parenthesys as a binomial squared:

$y=3(x+10)^2-450$

The option a) is the correct answer.