4. Polynomial Functions

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = x² + 6x + 5

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).

Connecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.)

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.

October

An equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=5x²−5x

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x²+3x−10

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$

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.

May

Consider the graph of each quadratic function.

a) Give the domain and range.

Several graphs of the quadratic function ƒ(x) = ax² + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; b² - 4ac = 0

Several graphs of the quadratic function ƒ(x) = ax² + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b² - 4ac > 0

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -(1/2)(x + 1)² - 3

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

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

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

Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x² or g(x) = -3x², but with the given maximum or minimum. Maximum = 4 at x = -2

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=(x−1)²+2