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Ksenya-84 [330]
3 years ago
5

When given a function in standard form,how can you determine if the parabola has aminimum or maximum value

Mathematics
1 answer:
andrezito [222]3 years ago
3 0

Answer:

It can be determined if a quadratic function given in standard form has a minimum or maximum value from the sign of the coefficient "a" of the function. A positive value of "a" indicates the presence of a minimum point while a negative value of "a" indicates the presence of a maximum point

Step-by-step explanation:

The function that describes a parabola is a quadratic function

The standard form of a quadratic function is given as follows;

f(x) = a·(x - h)² + k, where "a" ≠ 0

When the value of part of the function a·x² after expansion is responsible for the curved shape of the function and the sign of the constant "a", determines weather the the curve opens up or is "u-shaped" or opens down or is "n-shaped"

When "a" is negative, the parabola downwards, thereby having a n-shape and therefore it has a maximum point (maximum value of the y-coordinate) at the top of the curve

When "a" is positive, the parabola opens upwards having a "u-shape" and therefore, has a minimum point (minimum value of the y-coordinate) at the top of the curve.

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Mary and Jane both took PSY230 last semester but they were in two different sections taught by different professors. Mary's clas
Greeley [361]

Answer:

Due to the higher z-score, Jane did better in class.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Whoever's grade had the better z-score did better in class.

Mary's:

Mean of 85, standard deviation of 5, grade of 88. This means that \mu = 85, \sigma = 5, X = 88. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{88 - 85}{5}

Z = 0.6

Jane's

Mean of 80, standard deviation of 10, grade of 88. This means that \mu = 80, \sigma = 10, X = 88. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{88 - 80}{10}

Z = 0.8

Due to the higher z-score, Jane did better in class.

4 0
2 years ago
Carly owns a toy store. She sells teddy bears and charges $25 per bear. Her total monthly cost is $3765. How many bears does Car
Zinaida [17]

Answer:

divide 3765 by 25 to get how many bears she sold, then divide that by 3765

3 0
2 years ago
Read 2 more answers
The slope of the line y = 4x − 2 is:
Paladinen [302]

Answer: m = 4

Step-by-step explanation: This is a linear equation.

Linear equations can be written in the form y = mx + b where

the multiplier, m, represents the slope of the line and the <em>b</em>

or the constant term represents the y-intercept of the line.

So the slope of this line is simply the multiplier

which is the coefficient of the x term which is 4.

The variable that's used to represent slope is <em>m</em>.

So we say that m = 4.

6 0
3 years ago
Eugene wants to buy jeans at a store that is offering a $10 discount on every item. The tag on the jeans is marked 50% off. The
kifflom [539]
A. $14.99 .. do $49.98/2 = $24.99 and then subtract $10.
B. $19.99 .. do $49.98-19 = $39.98 and then divide it by 2.
3 0
3 years ago
If tan theta = 12/5 and cos theta &lt; 0, what is sin theta ?
Talja [164]
1 + tan ² Ф=sec²Ф
1+(12/5)²=sec²Ф
169/25=sec² Ф
sec Ф=⁺₋√(169/25)=⁺₋13/5

sec Ф=1/cos Ф ⇒cosФ=1/sec Ф
 cos Ф>0   ⇔  sec Ф>0  ⇔  sec Ф=+ 13/5

cos Ф=1/secФ
cos Ф=1 / 13/5=5/13

we can calculate the sin Ф, with this method.
sin²Ф + cos²Ф=1  ⇒ sin Ф=⁺₋√(1-cos² Ф)
sin Ф=⁺₋√[1-(5/13)²]=⁺₋12/13
like cos Ф>0 and tan Ф>0   ⇒ sin Ф>0 ⇒sin Ф=12/13

answer: d.12/13

other method
tan Ф=sin Ф / cos Ф
12/5=sin Ф / 5/13
sin Ф=(12/5)*(5/13)=12/13

answer: d.12/13

8 0
3 years ago
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