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Marizza181 [45]
3 years ago
15

What are the right answers to these questions? This is what I plugged in and I got them wrong.

Mathematics
1 answer:
strojnjashka [21]3 years ago
8 0

Answer:

Concave Upward: (0,2), (4,6), (7,12) (even though the slope changes at x = 9, the slope is still increasing from 9 to 12; notice its upward curve)

Concave Downward: (2, 4), (6, 7)

Inflection Points: (2,2), (4,2), (6,2), (7,3)

Step-by-step explanation:

Recall that concave upward is when the slope is increasing, and concave downward is when the slope is decreasing.

It seems that from your answers (for part a), you are looking for when the slope changes from positive to negative (and vice versa). These two things (the rate of change of the slope and the sign of the slope) are critically different, but are easy to confuse. In other words, you're basing your answers off of maxima and minima (high points and low points on the graph).

What you really want to base your answers on are inflection points, which are points where the slope goes from becoming increasingly more negative/positive to the other.

For example, look at x = 2 on the graph. If we draw a line tangent to the graph for every x, we will see that the line will become steeper and steeper until we reach x = 2, where it will slowly start to taper off until it becomes flat at x = 3. I encourage you to look up some videos on the topic of concavity, they will show it better then I could.

If you can't do that, you can use a ruler to visualize the tangent line as you move it across the graph. When you have to start turning the ruler in the opposite direction to keep it tangent to the graph, you found an inflection point.

Inflection points are points that are on the graph, so I encourage you to keep that in mind when you are answering problems similar to that in part b.

Here is a useful resource: https://www.mathsisfun.com/calculus/concave-up-down-convex.html

Best of luck!

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Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts.
jasenka [17]

Answer:

We have the function, f(x)=(x+3)^{2}-4

On simplifying, we get,

f(x)=x^2+6x+9-4

i.e. f(x)=x^2+6x+5

Thus, the standard form of the function is f(x)=x^2+6x+5.

Now, the factors of the given functions are (x+1) and (x+5).

<em>Since, the intercept form of the function is the factored form of the function.</em>

So, we have, intercept form of the function is f(x)=(x+1)(x+5).

Now, we know that,

Value of x-coordinate of the vertex is \frac{-b}{2a} i.e. \frac{-6}{2\times 1} i.e. \frac{-6}{2} i.e. x= -3

Then, f(-3)=(-3)^2+6\times (-3)+5 i.e. f(-3)=9-18+5 i.e. f(-3)=-4

So, the vertex of the function is (-3,-4).

Further, we know that,<em> 'the y-intercept of a function is the point where the function crosses y-axis'.</em>

So, when x=0, we have, f(0)=0^2+6\times 0+5 i.e. f(0) = 5

Thus, the y-intercept is (0,5)

Also, <em>'the x-intercept of a function is the point where the function crossese x-axis'.</em>

Then, for f(x)=0, we have 0=x^2+6x+5 i.e. 0=(x+1)(x+5) i.e. x= -1 and x= -5

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8 0
3 years ago
Please answer if you can 30 points.
Rudik [331]

Answer:

The y-intercept is 4

Step-by-step explanation:

You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).

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2 years ago
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3 years ago
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MAXImum [283]
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6 0
3 years ago
A used car was purchased in July 1999 for $11,900. If the car depreciates 13% of it's value each year, what is the value of the
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1999 price = 11900
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