Question

g is a quadratic function with the vertex at (-3, 2) and g(0) = - 34. Find an algebraic equation forg(u).

Answer 1

We are to find an algebraic equation for g(u), where g is a function with vertex at (-3, 2) and g (0) = - 34.

`\begin{gathered} y=a(x-h)^2\text{ + k} \\ y=a(x+3)^2\text{ + 2} \\ At\text{ (0, -34)} \\ -34=a(0+3)^2\text{ + 2} \\ -34=a(3)^2\text{ + 2} \\ -34\text{ = 9a + 2} \\ -34\text{ -2 = 9a} \\ -36\text{ = 9a} \\ or\text{ } \\ 9a\text{ = -36} \\ a\text{ = -4} \end{gathered}`

a = - 4, h = -3 and k = 2

`\begin{gathered} y=a(x-h)^2\text{ + 2} \\ y=-4(x-(-3))^2\text{ + 2} \\ y=-4(x+3)^2+2 \\ y\text{ }=-4(x^2+6x\text{ + 9) +2} \\ y=-4x^2\text{ -24x -36 +2} \\ y=-4x^2\text{ -24x -34} \end{gathered}`