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3 years ago

How to find the maximum or minimum value of a quadratic function?

Mathematics

1 answer:

kipiarov [429]3 years ago

6 0

Answer:

Vertex form

Step-by-step explanation:

You convert to vertex form a(x - b)^2 + c . The coordinates of the maxm/minm will be (b, c).

For example find minimum value of x^2 + 5x - 6:-

x^2 + 5x - 6

= (x + 2.5)^2 - 6.25 - 6

= (x + 2.5)^2 - 12.25

The coordinates of minimumm will be (-2.5, -12.25) The values of the minimum of the function is -12.25

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If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

8 0

3 years ago

Tom works for a company.

pashok25 [27]

Answer:

£765

Step-by-step explanation:

3 0

2 years ago

Which description does NOT guarantee that a trapezoid is isosceles?

babunello [35]

A trapezoid is isosceles if and only if

(1) The base angles are congruent

(2) The diagonals are congruent

(3) The opposite angles are supplementary

So the description does not guarantee that a trapezoid is isoceles for "Congruent bases".

3 0

3 years ago

the height in feet above the ground of an arrow after it is shot can be modeled by y=-16r^2+63r+4.Can the arrow pass over a tree

miss Akunina [59]

Answer:

yes

Step-by-step explanation:

y=-16r^2+63r+4

maximum value of y :

y'=0

-32r +63=0

r= 63/32

y = -16(63/32)²+63(63/32)+4

= -4 + 124 + 4 = 124 ft

124 > 68

the Arrow can pass over the tree

7 0

2 years ago

Find the amount of the payment for the sinking fund.

ohaa [14]

:)
The formula of the future value of annuity ordinary and solve for pmt
Pmt=58,000÷(((1+0.06÷2)^(2×2)
−1)÷(0.06÷2))=13,863.57

Hope it helps

8 0

2 years ago