Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. ƒ(x)=-3x²-12x-1

The graph of a quadratic function is given. Write the function's equation, selecting from the following options.

$f\left(x\right)=(x+1{)}^2-1g\left(x\right)=(x+1{)}^2+1$

$h\left(x\right)=(x-1{)}^2+1j\left(x\right)=(x-1{)}^2-1$

Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.

Fill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x² + 2x + 4 has x-coordinate ____ .

In Exercises 5–6, use the function's equation, and not its graph, to find (a) the minimum or maximum value and where it occurs. (b) the function's domain and its range. $f\left(x\right)=-x^2+14x-106$

The graph of a quadratic function is given. Write the function's equation, selecting from the following options.

$f\left(x\right)=x^2+2x+1g\left(x\right)=x^2-2x+1$

$h\left(x\right)=x^2-1j\left(x\right)=-x^2-1$

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V\left(x\right)$, where $V\left(x\right)=2x^2-32x+150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, $V\left(x\right)$ is modeled by $V\left(x\right)=31x-226$. Find the number of volunteers in each of the following months. Sketch a graph of $y=V\left(x\right)$ for January through December. In what month are the fewest volunteers available?

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V\left(x\right)$, where $V\left(x\right)=2x^2-32x+150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is modeled by $V\left(x\right)=31x-226$. Find the number of volunteers in each of the following months.

January