SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the standard vertex form for a quadratic equation.
[tex]\begin{gathered} y=a(x-h)^2+k \\ where\text{ }(h,k)\text{ is the vertex} \end{gathered}[/tex]
STEP 2: Get the vertex of the quadratic equation plotted
[tex]Vertex=(h,k)=(-1,2)[/tex]
STEP 3: Get the value of a
To get the value of a, we pick a random point on the graph. We pick:
[tex](x,y)=(0,3)[/tex]
Substitute the known values into the form in Step 1 to get the value of a as seen below:
[tex]\begin{gathered} 3=a(0-(-1))^2+2 \\ 3=a(1^2)+2 \\ 3=a+2 \\ 3-2=a \\ a=1 \end{gathered}[/tex]
STEP 4: Get the vertex form of the equation
[tex]\begin{gathered} a=1 \\ (h,k)=(-1,2) \\ \\ By\text{ substitution,} \\ y=1(x-(-1))^2+2 \\ y=1(x+1)^2+2 \end{gathered}[/tex]
Hence, the vertex form of the equation is given as:
[tex]f(x)=1(x+1)^2+2[/tex]
