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Which of the quadratic functions has the narrowest graph?

charle [14.2K]

Answer:

$y=\frac{1}{8}x^2$

Step-by-step explanation:

A quadratic function has the formula ax² + bx + c

To determine if a graph will be narrow or wide, the leading coefficient, a, will be the factor that determines this
The greater the coefficient, the narrower the parabola
The lesser the coefficient, the wider the parabola

Here all of the functions are in the form ax²

In $y=\frac{1}{8}x^{2}$ , our "a" term is $\frac{1}{8}$
In y = -2x², our "a" term is -2
In y = -3x², our "a" term is -3
In $y=\frac{1}{3}x^{2}$ , our "a" term is $\frac{1}{3}$

We can eliminate the two functions with the negative coefficients because they are much smaller than the two functions with the fractions as coefficients, and will therefore open much wider.

We can now compare the two remaining functions, $y=\frac{1}{8}x^2$ and $y=\frac{1}{3}x^2$

Giving the two fractions common denominators would turn them into $y = \frac{3}{24}x^2$ and $y=\frac{8}{24} x^2$
The equation with the larger fraction will be the parabola that is the narrowest. In this case, it is the $y=\frac{8}{24} x^2$ .
Therefore, $y=\frac{1}{8}x^2$ will have the narrowest graph

7 0

3 years ago

Mr. Cannon has a piece of land that is 3/7 of an acre. He wants to build 10 houses on his land. How much land does each house ge

sashaice [31]

Answer:

Step-by-step explanation:

3/7 divided by 10 houses= 0.042 acres per house

4 0

3 years ago

In how many ways can you place 50 identical balls in six distinct urns such that each urn contains an odd number of balls

mezya [45]

Answer:

80730

Step-by-step explanation:

The answer is c(27,5)=27*26*25*24*23/5!. Here is why.

Let us solve a simpler problem. In how many ways 25 identical balls can be placed in six distinct urns such that no urn is empty?

25 balls in a row make 24 places for five dividers, so the answer is c(24,5).

2. Next problem. In how many ways 50 identical balls can be placed in six distinct urns such that no urn is empty and each urn contains even number of balls.

We group 50 balls in 25 pairs, so the answer is the same as in the previous problem which is

c(48/2,5)=c(24,5).

Let us denote the content of each urn as

u(1),u(2),…u(6). Note that each u(i) is even. Denote u(i) as u(i)=2k(i) where k is a natural number. We have

2k(1)+2k(2)+2k(3)+2k(4)+2k(5)+2k(6)=50.

3. Now let us proceed to the original problem where odd number of balls in each urn is required.

We have

2k(1)-1+2k(2)-1+2k(3)-1+2k(4)-1+2k(5)-1+2k(6)-1=50 or

2k(1)+2k(2)+2k(3)+2k(4)+2k(5)+2k(6)=56.

So the original problem reduces to previous problem where even number of balls in each urn is required but the total number of balls is 56 instead of 50.

Its answer is c(54/2,5)=c(27,5).

8 0

3 years ago

If your bill was $67.82 and there is a 7.5% late fee how much is your bill

zaharov [31]

67.82 x .075 = 5.0865 rounded to 5.09. 5.09+ 67.82 = $72.91. There's your answer

7 0

3 years ago

What is the missing term? (10x – 4x2) – (7x + ?) = 3x – 6x2

tino4ka555 [31]

Answer:

Step-by-step explanation:

2x squared ^c^

5 0

4 years ago

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