For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of f is above or below the x-axis. Determine the y-intercept. Find any symmetries of the graph. Determine the maximum possible number of turning points. Finally, sketch the graph of f. Using a graphing utility to determine any relative maximums and minimums.

you must have some ideas about some of these topics. At the very least, use a graphing utility to see what the graph looks like, and most of the answers should become clear immediately.

determine the y-intercept of f(x)=-1/8(x-7)(x+9), then graph this function on the grid provided. Label any points you plot with the ordered pair.

To find the y-intercept of the function f(x) = -1/8(x-7)(x+9), we can substitute x = 0 into the equation and solve for y.

f(0) = -1/8(0-7)(0+9)
= -1/8(-7)(9)
= -1/8 * (-63)
= 63/8

Therefore, the y-intercept of the function f(x) is (0, 63/8).

To graph the function, we can plot a few more points and connect them to get an accurate representation of the graph.

Let's choose x = -9, -7, and 7 as the test points.

For x = -9:
f(-9) = -1/8(-9-7)(-9+9)
= -1/8(-16)(0)
= 0

Therefore, the point (-9, 0) is on the graph.

For x = -7:
f(-7) = -1/8(-7-7)(-7+9)
= -1/8(-14)(2)
= -1/8 * (-28)
= 28/8
= 7/2

Therefore, the point (-7, 7/2) is on the graph.

For x = 7:
f(7) = -1/8(7-7)(7+9)
= -1/8(0)(16)
= 0

Therefore, the point (7, 0) is on the graph.

Now we can plot these points, along with the y-intercept (0, 63/8), on the grid provided and connect them to create the graph.

Please note that without a specific grid provided, we cannot physically draw the graph here. However, you can use these instructions to create the graph on a graphing utility or draw it by hand on a graph paper.

vertex of f(x)=-1/8(x-7)(x+9), then graph this function on the grid provided. Label any points you plot with the ordered pair.

To find the vertex of the function f(x) = -1/8(x-7)(x+9), we can use the vertex formula for a quadratic function: x = -b/(2a), where the equation is in the form f(x) = ax^2 + bx + c.

In this case, a = -1/8, b = 0 (since there is no x term), and c = 0. Plugging these values into the vertex formula, we have:

x = -0/(2*(-1/8))
x = 0/(-1/4)
x = 0

So the x-coordinate of the vertex is 0. Now we can substitute x = 0 into the function to find the y-coordinate:

f(0) = -1/8(0-7)(0+9)
= -1/8(-7)(9)
= -1/8 * (-63)
= 63/8

Therefore, the vertex of the function f(x) is (0, 63/8).

To graph the function, we can plot a few more points and connect them to get an accurate representation of the graph.

Let's choose x = -9, -7, and 7 as the test points.

For x = -9:
f(-9) = -1/8(-9-7)(-9+9)
= -1/8(-16)(0)
= 0

Therefore, the point (-9, 0) is on the graph.

For x = -7:
f(-7) = -1/8(-7-7)(-7+9)
= -1/8(-14)(2)
= -1/8 * (-28)
= 28/8
= 7/2

Therefore, the point (-7, 7/2) is on the graph.

For x = 7:
f(7) = -1/8(7-7)(7+9)
= -1/8(0)(16)
= 0

Therefore, the point (7, 0) is on the graph.

Now we can plot these points, along with the vertex (0, 63/8), on the grid provided and connect them to create the graph.

Please note that without a specific grid provided, we cannot physically draw the graph here. However, you can use these instructions to create the graph on a graphing utility or draw it by hand on a graph paper.

determine the y-intercept of f(x)=0.2(x-5)^2 - 8, then graph this function on the grid provided. Label any points you plot with the ordered pair.

To find the y-intercept of the function f(x) = 0.2(x-5)^2 - 8, we can substitute x = 0 into the equation and solve for y.

f(0) = 0.2(0-5)^2 - 8
= 0.2(-5)^2 - 8
= 0.2 * 25 - 8
= 5 - 8
= -3

Therefore, the y-intercept of the function f(x) is (0, -3).

To graph the function, we can plot a few more points and connect them to get an accurate representation of the graph.

Let's choose x = 3, 5, and 7 as the test points.

For x = 3:
f(3) = 0.2(3-5)^2 - 8
= 0.2(-2)^2 - 8
= 0.2 * 4 - 8
= 0.8 - 8
= -7.2

Therefore, the point (3, -7.2) is on the graph.

For x = 5:
f(5) = 0.2(5-5)^2 - 8
= 0.2(0)^2 - 8
= 0.2 * 0 - 8
= 0 - 8
= -8

Therefore, the point (5, -8) is on the graph.

For x = 7:
f(7) = 0.2(7-5)^2 - 8
= 0.2(2)^2 - 8
= 0.2 * 4 - 8
= 0.8 - 8
= -7.2

Therefore, the point (7, -7.2) is on the graph.

Now we can plot these points, along with the y-intercept (0, -3), on the grid provided and connect them to create the graph.

Please note that without a specific grid provided, we cannot physically draw the graph here. However, you can use these instructions to create the graph on a graphing utility or draw it by hand on a graph paper.

vertex of f(x)=0.2(x-5)^2 - 8, then graph this function on the grid provided. Label any points you plot with the ordered pair.

The given function is f(x) = 0.2(x-5)^2 - 8.

To find the vertex of the function, we can use the vertex formula for a quadratic function: x = -b/(2a), where the equation is in the form f(x) = ax^2 + bx + c.

In this case, a = 0.2, b = 0 (since there is no x term), and c = -8. Plugging these values into the vertex formula, we have:

x = -0/(2*0.2)
x = 0/0.4
x = 0

So the x-coordinate of the vertex is 0. Now we can substitute x = 0 into the function to find the y-coordinate:

f(0) = 0.2(0-5)^2 - 8
= 0.2(-5)^2 - 8
= 0.2 * 25 - 8
= 5 - 8
= -3

Therefore, the vertex of the function f(x) is (0, -3).

To graph the function, we can plot a few more points and connect them to get an accurate representation of the graph.

Let's choose x = 1, 3, 5, 7, and 9 as the test points.

For x = 1:
f(1) = 0.2(1-5)^2 - 8
= 0.2(-4)^2 - 8
= 0.2 * 16 - 8
= 3.2 - 8
= -4.8

Therefore, the point (1, -4.8) is on the graph.

For x = 3:
f(3) = 0.2(3-5)^2 - 8
= 0.2(-2)^2 - 8
= 0.2 * 4 - 8
= 0.8 - 8
= -7.2

Therefore, the point (3, -7.2) is on the graph.

For x = 5:
f(5) = 0.2(5-5)^2 - 8
= 0.2(0)^2 - 8
= 0.2 * 0 - 8
= 0 - 8
= -8

Therefore, the point (5, -8) is on the graph.

For x = 7:
f(7) = 0.2(7-5)^2 - 8
= 0.2(2)^2 - 8
= 0.2 * 4 - 8
= 0.8 - 8
= -7.2

Therefore, the point (7, -7.2) is on the graph.

For x = 9:
f(9) = 0.2(9-5)^2 - 8
= 0.2(4)^2 - 8
= 0.2 * 16 - 8
= 3.2 - 8
= -4.8

Therefore, the point (9, -4.8) is on the graph.

Now we can plot these points, along with the vertex (0, -3), on the grid provided and connect them to create the graph.

Please note that without a specific grid provided, we cannot physically draw the graph here. However, you can use these instructions to create the graph on a graphing utility or draw it by hand on a graph paper.

determine the y-intercept of f(x)=-1/8(x-7)(x+9), in graph