At Home Part 4 Answers

How many active volcanoes are there in Nicaragua?

The zeros of a parabola are 6 and −5. If (-1, 3) is a point on the graph, which equation can be solved to find the value of a in the equation of the parabola?

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Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?

Factor x2 – 8x + 15. | Which pair of numbers has a product of ac and a sum of b? | What is the factored form of the trinomial?

How is the rainforest in Nicaragua ranked in the Americas?

Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)?

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.The value of f(–10) = 82The graph of the function is a parabola.The graph of the function opens down.The graph contains the point (20, –8).The graph contains the point (0, 0).

According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x?

Factor x2 – 8x + 15. | Which pair of numbers has a product of ac and a sum of b? | What is the factored form of the trinomial?

What percentage of Nicaragua's territory is protected as National Parks or Biological Reserves?

On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.Time (x) Height (y) 0102241610How high was the ball after 8 seconds?

The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?

The function f(x) = −(x + 5)(x + 1) is shown.

Other than Spanish, what language is spoken in Nicaragua?

Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.

On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.7, negative 2.75), and goes through (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.5, negative 2.75), (3, negative 2), (6, 4).

Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g(x) = –x2 + 16x – 44?

How many craters does the Masaya volcano have?

The graph shows the function representing the recommended amount of mulch, in cubic yards, for circular flowerbeds based on the radius of the flowerbed in feet.

Which is the graph of the function f(x) = x2 + 2x + 3?

What is the axis of symmetry for the function f(x)=7−4x+x2?

The height of a hill, h(x), in a painting can be written as a function of x, the distance from the left side of the painting. Both h(x) and x are measured in inches.

The graph of the function f(x) = (x + 2)(x − 4) is shown.

Which quadratic function is the standard form of the equation shown?f(x) = x + 8 + 2x + 5x2

The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far away from the maximum depth is a point on the mirror that is inches in depth?

What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?

Which point is an x-intercept of the quadratic functionf(x) = (x – 8)(x + 9)?

The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground?

The function f(x) = –x2 – 4x + 5 is shown on the graph.

Which is the graph of f(x) = x2 – 2x + 3?

The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?

Given the function f(x) = −5x2 − x + 20, find f(3).

The vertex of a quadratic function is (6, 2), and the y-intercept of the function is (0, −70). The equation of the function in vertex form, f(x)=a(x−h)2+k, is shown.−70=a(0−6)2+2

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The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.Write the function in standard form.f(x) = 5x2 + 40xFactor a out of the first two terms.f(x) = 5(x2 + 8x)Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) – 5(16)What is the function written in vertex form?

Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?

What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.

The function f(x) = –(x – 3)2 + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 9x2 – 36x?

A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 3, negative 2, negative 3, 0, 7.

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6?

Mary throws a plastic disc to her friend. Her friend catches the disc six seconds after Mary throws it. The table shows the height of the disc at one-second intervals.

On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.75, negative 2.75), and goes through (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.75, negative 2.75), (3, negative 2), (6, 4).

On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).

Which function in vertex form is equivalent to f(x) = x2 + x +1?

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

The graph of the function f(x) = –(x + 3)(x – 1) is shown below.

What are the x-intercepts of the function f(x) = –x2 – x + 2?

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.f(x) = 4(x2 + 12x) + 10 = 36

Consider the function shown on the graph.

Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16)?

An algebra tile configuration. Only the Product spot is shown. 8 tiles are in the Product spot in 3 columns with 3 rows. First row: 1 + x squared, 2 + x. Second row: 1 +x, 2 +. Third row: 1 +x, 1 +.

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?

The graph of the function f(x) = (x + 2)(x + 6) is shown below.