4. Polynomial Functions

Identify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.

Where is the axis of symmetry located on the given parabola? 

Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\(\left\)(x\(\right\))=-\(\left\)(x-5\(\right\))^2+1$

Graph the given quadratic function. Identify the vertex, axis of symmetry, intercepts, domain, range, and intervals for which the function is increasing or decreasing. $f\(\left\)(x\(\right\))=3x^2+12x$

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

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

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

In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range.

$f\left(x\right)=-(x+1{)}^2+4$

In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x) = (x + 4)^2 - 2

In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $f\left(x\right)=-x^2+2x+3$