Question

Number 11 please write the equation for the standard function use transformations and critical points of the graph

Answer 1

Solution

- The formula for the vertex form of a quadratic equation is given below:

$\begin{gathered} y=a(x-h)^2+k \\ where, \\ (h,k)\text{ is the coordinate of the vertex} \end{gathered}$

- The vertex of the quadratic equation is depicted below:

- Thus, the vertex of the quadratic graph is V(2, -2).

- The equation of the graph becomes:

$y=a(x-2)-2$

- To find the value of "a", we apply the coordinate given (-1, 6). This is done below:

$\begin{gathered} when\text{ }x=-1,y=6 \\ \\ 6=a(-1-2)^2-2 \\ 6=a(-3)^2-2 \\ 6=9a-2 \\ \text{ Add 2 to both sides} \\ 9a=8 \\ \text{ Divide both sides by -3} \\ \\ a=\frac{8}{9} \end{gathered}$

Final answer

The equation is:

$y=\frac{8}{9}(x-2)^2-2$