4. Polynomial Functions

In Exercises 17–38, 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+6x+3

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)=2x−x²+3

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.

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

Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x + 4)² - 3

The distance between the two points $P(x_1,y_1)$ and $R(x_2,y_2)$ is $d(P, R) = \(\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)$. Distance formula. Find the closest point on the line $y=2x$ to the point $(1,7)$. (Hint: Every point on $y=2x$ has the form $(x,2x)$, and the closest point has the minimum distance.)

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.

December

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. y−1=(x−3)²

A quadratic equation ƒ(x) = 0 has a solution x = 2. Its graph has vertex (5, 3). What is the other solution of the equation?

Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)² - 3

Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x² but with the given point as the vertex. (−10, −5)

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -3 (x - 2)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(x) is modeled by $V\left(x\right)=31x-226$. Find the number of volunteers in each of the following months.

January