I’m very confused pls help 50 PTSFind the quadratic function y=ax^2 +bx+c whose graph passes through the given points. (-1,-11) (2,-26) (-3,-31)
Answers
The quadratic value function is y = -x² - 4x + 16
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
Let the function passes through the given points. (-1,-11) (2,-26) (-3,-31)
And , using the point (-1,-11) , we get
-11 = a(-1)² + b(-1) + c
-11 = a - b + c
Using the point (2,-26) , we get
-26 = a(2)² + b(2) + c
-26 = 4a + 2b + c
Using the point (-3,-31) , we get
-31 = a(-3)² + b(-3) + c
-31 = 9a - 3b + c
And , the three set of equations are
-11 = a - b + c
-26 = 4a + 2b + c
-31 = 9a - 3b + c
From the first equation, we can solve for c:
c = 11 - a + b
Substituting this expression for c into the other two equations, we get:
-26 = 4a + 2b + 11 - a + b
-31 = 9a - 3b + 11 - a + b
Simplifying these equations, we get:
-15 = 3a + 3b
-21 = 8a - 2b
Solving the first equation for b in terms of a, we get:
b = -5 - a
Substituting this expression for b into the second equation, we get:
-21 = 8a - 2(-5 - a)
Simplifying and solving for a, we get:
a = -1
Substituting this value of a into the equation for b that we found earlier, we get:
b = -5 - (-1) = -4
Finally, substituting these values of a and b into the equation for c that we found earlier, we get:
c = 11 - (-1) - (-4) = 16
Hence , the quadratic function that passes through the given points is given by y = -x² - 4x + 16
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Related Questions
The amount of cereal in a box is normal with mean 16.5 ounces. If the packager is required to fill at least 90% of the cereal boxes with 16 or more ounces of cereal, what is the largest standard deviation for the amount of cereal in a box?
Which letter represents the maximum of the data set on the box plot?
Solve for e.9e + 4 = -5e + 14 + 13e
Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children find the probability of at most three boys in ten births
Answers
Answer:
The x-values of the inflection points of the curve are x = -52 and x = 52.
Step-by-step explanation:
Suppose we have a normal curve with mean and standard deviation
The x-values of the inflection points of the curve are and
x ~ N(0, 52)
This means that
So
The x-values of the inflection points of the curve are x = -52 and x = 52.
Final answer:
The inflection points in a normal distribution occur at one standard deviation above and below the mean. For the distribution x ~ N(0, 52), the inflection points are at -√52 and √52.
Explanation:
In a normal distribution, the inflection points occur at one standard deviation above and below the mean. In the given normal distribution, x ~ N(0, 52), the mean (μ) is 0 and the standard deviation (σ) is the square root of the variance, i.e., √52.
Therefore, the x-values for the inflection points would be μ - σ and μ + σ, which are -√52 and +√52, respectively.
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Answers
The fractions is solved and the improper fraction is A = 29/8
Given data ,
To change 3 5/8 into an improper fraction, we need to combine the whole number and the fraction part.
The fraction part, 5/8, can be expressed as an improper fraction by multiplying the whole number, 3, by the denominator of the fraction, 8, and then adding the numerator, 5. This gives us:
3 * 8 + 5 = 24 + 5 = 29
The denominator remains the same, so the improper fraction is:
A = 29/8
Therefore , the value of A = 29/8
Hence , 3 5/8 can be expressed as the improper fraction 29/8
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Answer:
The improper fraction 29/8 is equal to the mixed number 3 5/8.
Step-by-step explanation:
Answers
Answer:
speed=200 m/s
Step-by-step explanation:
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Answer: irdk the awnser but F on that tumor
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Answer:
k < -2
Step-by-step explanation:
Step 1: Write inequality
4k + 2(3k + 8) < 3k + 10 - 8
Step 2: Solve for k
- Distribute: 4k + 6k + 16 < 3k + 10 - 8
- Combine like terms: 10k + 16 < 3k + 2
- Subtract 3k on both sides: 7k + 16 < 2
- Subtract 16 on both sides: 7k < -14
- Divide both sides by 7: k < -2
Answer:
10k+16<3k+2
10k-3k+16<2
7k<2-16
k<-2
Answers
Answer:
19.80 in
Step-by-step explanation:
The Pythagorean theorem tells you ...
28² = x² + x²
28² = 2x² . . . . . collect terms
28 = (√2)x . . . . take the square root
28/√2 = x ≈ 19.79899 ≈ 19.80 . . . . . divide by the coefficient of x and round (dimensions are in inches)