determine the equation of the parabola whose graph is given below. enter your answer in general form.

Explanation:

Step1: Identify vertex form

The vertex - form of a parabola is $y=a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. From the graph, the vertex $(h,k)=(2,1)$. So the equation becomes $y=a(x - 2)^2+1$.

Step2: Find the value of a

The parabola passes through the point $(3,0)$. Substitute $x = 3$ and $y = 0$ into $y=a(x - 2)^2+1$. [ \begin{align*} 0&=a(3 - 2)^2+1\ 0&=a\times1^2+1\ 0&=a + 1\ a&=- 1 \end{align*} ]

Step3: Convert to general form

Substitute $a=-1$ into $y=a(x - 2)^2+1$. [ \begin{align*} y&=-(x - 2)^2+1\ y&=-(x^{2}-4x + 4)+1\ y&=-x^{2}+4x-4 + 1\ y&=-x^{2}+4x-3 \end{align*} ]

Answer:

$y=-x^{2}+4x - 3$