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taurus [48]
3 years ago
15

Without drawing the graph of the equation, determine how many points the given equation have in common with the x-axis and where

is the vertex in relation to the x-axis?
y = -2x^2 + x + 3

Mathematics
1 answer:
Gala2k [10]3 years ago
4 0
Remark
It's asking you to complete the square to find the vertex. 

Solve
y = -2x^2 + x + 3 Put brackets around the first 2 terms.
y = (-2x^2 + x) + 3    Pull out the 2.
y = -2(x^2 - 1/2 x) + 3 Be especially observant of the sign on 1/2x Divide the middle term's number by 2 and square it. 
y = -2(x^2 - 1/2 x + [(1/2) / 2]^2 ) + 3 [1/2 divided by 2 is 1/4. (1/4)^2 = 1/16; 2*(1/16) = 1/8
y = - 2(x^2 - 1/2 x + (1/4)^2 ) + 3 + 1/8
y = -2(x - 1/4)^2 + 3 1/8

Comment
Answer to your question. The maximum value (3 1/8) is above the y axis. That means the graph of the equation crosses the x axis twice. I'm going to include the graph because in answering the question, there is no harm in seeing the graph.

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Please help!!! ill mark brainliest
Vesnalui [34]

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2 - 8x = 2 - 8x

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add x to both sides, subtract 1 from both sides, and divide both sides by 2 to get  (x = \frac{3}{2} ). This statement is true only when x = \frac{3}{2} so it is: CONDITIONAL

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sasho [114]
Answer is 54^2.

since there are triangles in this one, it is easier to do this. all you have to do is make boxes in and since there are angles, outside the lines. like this picture.

the orange is 1
red and dotted is 2
blue is 3
purple is 4(a regular box which should be easy to count.

all you have to do is add up all the boxes within the boundaries.
boundary 1: 12
boundary 2: 18
boundary 3: 6
boundary 4: 36

now when the boundary has a triangle in it (1, 2, & 3) divide the number you got in half or 2.
boundary 1: 6
boundary 2: 9
boundary 3: 3

the ractangle box doesn't not get divided.
boundary 1: 6
boundary 2: 9
boundary 3: 3
boundary 4: 36

add all the numbers you got now for each boundary and that would be your area squared.

6+9+3+36=54^2

so your final answer is 54^2.

i hope this helps you.

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Answer:


Step-by-step explanation:

a. Profit, p, earned from selling x hats when hat will be sold for $12 each:

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b. To recover the cost of making the 200 hats which is $1500, profit, p >= cost:

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