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tamaranim1 [39]
4 years ago
6

Use the function f(x) to answer the questions: f(x) = 2x2 − x − 10

Mathematics
1 answer:
Sidana [21]4 years ago
6 0

Answer:

A. x = -2, 5/2

B. Minimum

Vertex: (1/4, -81/8)

C. Draw a concave up graph connecting the x-intercepts, vertex and the y-intercept

Step-by-step explanation:

f(x) = 2x² - x - 10

2x² - x - 10 = 0

2x² - 5x + 4x - 10 = 0

x(2x - 5) + 2(2x - 5) = 0

(x + 2)(2x - 5) = 0

x = -2, 5/2

Vertex: (h,k)

h = midpoint of the x-intercepts (due to symmetry)

h = (-2 + 5/2) = 1/4

k = f(1/4)

k = 2(1/4)² - 1/4 - 10 = -81/8

Vertex: (1/4, -81/8)

y-intercept: when x = 0

2(0)² - 0 - 10 = -10

Draw a concave up quadratic connecting thr following points:

(-2,0)

(0,-10)

(1/4,-81/4)

(5/2,0)

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Find the distance between the points (4,-2) and (0,10)
vagabundo [1.1K]

We can solve this problem by using the distance formula. The distance formula is: \sqrt{(x_{1}-x)^{2} + (y_{1} - y)^{2}} We can now put in values and solve.

\sqrt{(4-0)^{2} + (-2-10)^{2}}  

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3 0
3 years ago
F(x)=6x-18 sub in f(x/3), f(x)/3
arlik [135]

These are two separate problems: in the first we will have to substitute in a new value for x into the original equation and in the second we will manipulate the preexisting equation for f(x).

To begin, we will sub in f(x/3). To do this, we will substitute each variable x in the equation (in this case there is only one) with x/3, and then simplify the resulting equation.

f(x) = 6x - 18

f(x/3) = 6(x/3) - 18

To simplify, we should distribute the 6 on the right side of the equation.

f(x/3) = 6x/3 - 18

Now, we can divide the first term on the right side to finalize our simplification.

f(x/3) = 2x -18

Secondly, we are asked to find f(x)/3. To do this, we will take our original value for f(x), and then simplify divide that entire function by 3.

f(x) = 6x - 18

f(x)/3 = (6x-18)/3

This means that we must divide each term of the binomial by 3, so we are really computing

f(x)/3 = 6x/3 - 18/3

We can simplify by dividing both of the terms.

f(x)/3 = 2x - 6

Therefore, your answer is that f(x/3) = 2x - 18, but f(x)/3 = 2x - 6. It is important to recognize that these are two similar, yet different, answers.

Hope this helps!


8 0
3 years ago
Kim spent $33 on a magazine and
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Answer:

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Suppose the number of candy bars purchased is x

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Hope this helps! :)

5 0
3 years ago
Read 2 more answers
What is the smallest 3-digit palindrome that is divisible by both 3 and 4?
kirill [66]

Answer:

252

Step-by-step explanation:

To be divisible by 3, it's digits have to add to a number that is a multiple of 3.

To be divisible by 4 its last 2 digits have to be divisible by 3.

So let's start with 1x1 which won't work because 1x1 is odd. so let's go to 2x2 and see what happens.

212 that's divisible by 4 but not 3

222 divisible by 3 but not 4

232 divisible by 4 but not 3

242 not divisible by either one.

252 I think this might be your answer

The digits add up to 9 which is a multiple of 3 and the last 2 digits are divisible by 4

4 0
3 years ago
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