Question

6. Write a quadratic function whose graph has a vertex of (-4,-2) and passes through the point (-3,1).

Answer 1

`y=a(x-h)^2+k`

(h,k) are the coordinates of the vertex.

Use the given point (x,y) and the vertex (h,k) in the equation above to find the value of a:

Point: (-3 ,1) x = -3 y=1

Vertex: (-4 , -2) h= -4 k=-2

`\begin{gathered} 1=a(-3-(-4))^2+(-2) \\ 1=a(-3+4)^2-2 \\ 1=a(1)^2_{}-2 \\ 1=a-2 \\ 1+2=a \\ 3=a \end{gathered}`

Use the vertex and a to write the equation:

`\begin{gathered} y=3(x-(-4))^2+(-2) \\ \\ \\ y=3(x+4)^2-2 \end{gathered}`