How do the average rates of change for each pair of functions compare over the given interval? f(x) = -2x², g(x) = -4x², -4 ≤ x ≤ -2

A disc is thrown into the air with an upward velocity of 20 ft/s. Its height h in feet after t seconds is given by the function h = -16t² + 20t + 6. What is the maximum height the disc reaches? How long will it take the disc to reach the maximum height? How long does it take for the disc to be caught 3 feet off the ground?

How does the value of a in each function affect its graph when compared to the graph of the quadratic parent function? C(x) = 0.04x²

The total cost, in dollars, of a square carpet can be determined by using f(x) = 15x², where x is the side length in yards. Which of the following are true? Select all that apply. A. The cost of a carpet increases and then decreases as the side length increases. B. The cost of the carpet is $15 per square yard. C. The cost of a carpet with a side length of 3 yd is$135. D. The cost of a carpet with 6-ft sides is twice the cost of a carpet with 3-ft sides. E. The cost of a carpet increases at a constant rate as the side length increases.

The graph of f(x) = ax² opens downward and is narrower than the graph of the quadratic parent function. Which of the following could be the value of a? A. -2 B. -0.5 C. 0.5 D. 1 E. 2

Use the table to describe the intervals over which $f(x)=15x^2$ is increasing and decreasing.

$x$	$f(x)=15x^2$	$(x,y)$
$-2$	$60$	$(-2,60)$
$-1$	$15$	$(-1,15)$
$0$	$0$	$(0,0)$
$1$	$15$	$(1,15)$
$2$	$60$	$(2,60)$

Find the y-intercept, the axis of symmetry, and the vertex of the graph of each function. f(x) = x² - 6x + 12

Tell whether each statement is always, sometimes, or never true. If the graph of a quadratic function has its vertex at the origin, then the related quadratic equation has exactly one solution.

Tell whether each statement about a function of the form f(x) = ax² is always true, sometimes true, or never true. a. The graph is a parabola that opens upward. b. The vertex of the graph is (0, 0). c. The axis of symmetry of the graph is x = 0.

Which type of function would best model the cost for carpeting a square room as a function of the room's width? Explain your answer.

The following chart rates movies according to certain categories. Four stars is the best rating, one star is the worst rating. Using the chart as a guide, write complete sentences comparing the three movies.
director/ "Siete meses en Lima"

Los premios Oscar.

The following chart rates movies according to certain categories. Four stars is the best rating, one star is the worst rating. Using the chart as a guide, write complete sentences comparing the three movies.

fotografia/ "Una tarde en agosto"

Make a conjecture about why the term quadratic parent function includes the word "parent."

How is the graph of f(x) = ax^2 similar to the graph of f(x) = x^2? How is it different?