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Yuki888 [10]
3 years ago
11

Write the equation in standard form of the quadratic that has a root of (3,0) and a vertex at (1,-4), then list out the values o

f a,b and c.
Mathematics
1 answer:
atroni [7]3 years ago
8 0

Answer:

a = 1, b = -2, c = -3

Step-by-step explanation:

The equation in <u>factored form</u> shows the roots with the "r" and "s" variables. Note that they are written <u>negative "r"</u> and <u>negative "s"</u> in the formula.

y = a(x - r)(x - s)

The <u>vertex is always halfway between the two roots</u>.

<------[root]--------[vertex]--------[root]---->

The vertex is at x = 1, and one root is at x = 3. The other root is at x = -1.

Write the equation in factored form to show the two roots.

y = a(x - 3)(x + 1)

<u>Substitute the vertex (1, -4)</u> into the equation. The point is written (x, y).

-4 = a(1 - 3)(1 + 1)

Solve for "a".

-4 = a(-2)(2)      Simplify within the brackets

-4 = -4a          Multiply -2 and 2. Divide both sides by -4

a = 1             Solved for "a" (and kept the variable on the left side).

<u>Substitute a = 1</u> back into the formula.

y = a(x - 3)(x + 1)

y = 1(x - 3)(x + 1)

We don't have to write multiplied by 1 though, because anything multiplied by 1 is itself.

y = (x - 3)(x + 1)

Since we are looking for "a", "b", and "c", find the equation in <u>standard form</u>.

y = ax² + bx + c

To change factored form into standard form, <u>expand</u> the brackets.

y = (x - 3)(x + 1)

y = x² + x - 3x - 3

y = x² - 2x - 3

Compare the expanded equation to y = ax² + bx + c

∴ a = 1, b = -2, c = -3

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7-ounce package costs $2.59. A 12 ounce package costs $4.56. An 18 ounce package costs $6.30. Which package is the best buy?
Yanka [14]

Answer:

18 ounce package for $6.30

Step-by-step explanation:

For each one, you divide the money by the package to see how much it is per ounce.

2.59 / 7 = $0.37 per oz

4.56 / 12 = $0.38 per oz

6.30 / 18 = $0.35 per oz

4 0
3 years ago
Jake made a wooden cone with a diameter of 6 inches and a height of 4.5 inches. What is the volume of this cone?
serious [3.7K]

Answer:

42.42in³

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

Step one

We know that the volume of a cone is

V= 1/3πr²h

Given data

Diameter d= 6 inches

Radius r= diameter/2= 6/2= 3 inches

Height h = 4.5 inches

Step two

Substituting our given data we have

Volume = 1/3*3.142*3²*4.5

V= 1/3*3.142*9*4.5

V= 127.251/3

V= 42.42in³

7 0
3 years ago
Look at the figure find the value of x for which l || m
Orlov [11]

Answer:

x=5

Step-by-step explanation:


19x and its vertical angle are equal.  Lets call that angle y

<y and 17x are same side interior angles.  Same side interior angles add to 180 if the lines are parallel.  Since l is parallel to m.

<y + 17x=180

We know that y and 19x are equal since they are vertical angles, so we can substitute this in.

19x+ 17x = 180

Combine like terms.

36x = 180

Divide each side by 36

36x/36 = 180/36

x = 5

8 0
3 years ago
Proving Angles Congruent: Find the value of x. (5x+15) degrees = (6x-10) degrees
Andrew [12]

Answer:

25 = x

Step-by-step explanation:

If the angles are congruent, they are equal

5x+15 = 6x-10

Subtract 5x from each side

5x+15 -5x = 6x-5x-10

15 = x-10

Add 10 to each side

15+10 = x-10+10

25 = x

6 0
3 years ago
Read 2 more answers
Mary is using a one-sample t-test on the following group:Subject #15: 7.5 hoursSubject #27: 6 hoursSubject #48: 7 hoursSubject #
elena-14-01-66 [18.8K]

Based on the information given, the correct options will be:

a.) Mary would use the sample standard deviation to calculate a t-statistic.

c.) The value for the degrees of freedom for Mary's sample population is six.

One-sample t-test simply means a statistical hypothesis test that's used for the determination of whether an unknown population mean will be different from the specific value.

In this case, the value of the degree of freedom for the sample will be:

= (n - 1) = 7 - 1 = 6.

Also, it should be noted that Mary would use the sample standard deviation to calculate a t-statistic.

Learn more about statistics on:

brainly.com/question/15525560

6 0
2 years ago
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