write the equation of the function whose graph is shown.\n$y = \\square(x + \\square)^2 + \\square$\ndone

Explanation:

Step1: Identify vertex form

The vertex form of a quadratic function is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex.

Step2: Substitute vertex coordinates

The vertex is $(5,3)$, so $h=5$, $k=3$. Substitute into the formula: $y=a(x-5)^2+3$

Step3: Solve for $a$ using given point

Use the point $(8,12)$: substitute $x=8$, $y=12$ $12=a(8-5)^2+3$ $12=9a+3$ $9a=9$ $a=1$

Step4: Rewrite to match given format

Rewrite $y=1(x-5)^2+3$ as $y=1(x+(-5))^2+3$ to fit $y=\square(x+\square)^2+\square$.

Answer:

$y = 1(x + (-5))^2 + 3$ (The blanks are filled with 1, -5, 3 respectively)