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. $f\left(x\right)=-x^2+2x+3$

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 ____ .

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

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

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

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.

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

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