Question

determine the equation of the parabola (simplified) with roots -3+sqrt6 and -3-sqrt6, and passing through the point (-1,4)

Answer 1

Given:

Roots:

`\begin{gathered} -3+\sqrt[]{6} \\ -3-\sqrt[]{6} \end{gathered}`

Point: (-1,4)

To determine the equation of the parabola with the given roots and point, we find the missing values first.

Since the roots are given, we can say that the equation is:

`y=a(x+3-\sqrt[]{6})(x+3+\sqrt[]{6})`

Next, we expand the terms.

`y=a(x^2+6x+3)`

Then, we plug in x= -1, and y=4 into the equation to get the value of a.

`\begin{gathered} y=a(x^2+6x+3) \\ 4=a((-1)^2+6(-1)+3) \\ \text{Simplify and rearrange} \\ 4=a(-2) \\ a=(4)/(-2) \\ a=-2 \end{gathered}`

So,