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posledela
2 years ago
15

The quadratic function f(x)=ax^2+4x+c has a maximum at the point (1, 9) . What are the values of a and c?

Mathematics
2 answers:
valina [46]2 years ago
6 0

Answer: a = -2  and  c = 7

Step-by-step explanation:

(this answer uses some basic calculus)

We know that f'(x) = 2ax + 4, and since (1,9) is a maximum of f, then f'(1) = 0. That means 2a + 4 = 0, so \boxed{a = -2}. Then since f(1) = 9, we have -2(1)^2 + 4(1) + c = 9, so \boxed{c = 7}.

valina [46]2 years ago
5 0

Answer:

a = -2

c = 7

Step-by-step explanation:

Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.

<h3>Solve for the value of <em>a</em>:</h3>

Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, x = \frac{-b}{2a}:

We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of <em>a</em>:

x = \frac{-b}{2a}

1 = \frac{-4}{2a}

Multiply both sides by 2a:

(2a) 1 =  \frac{-4}{2a} (2a)

2a = -4

Divide both sides by 2 to solve for a:

\frac{2a}{2} = \frac{-4}{2}

a = -2

Therefore, the value of a = -2.

<h3>Solve for the value of c:</h3>

Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:

f(x) = ax² + 4x + c

9 = -2(1)² + 4(1) + c

9 = -2 + 4 + c

9 = 2 + c

Subtract 2 from both sides to isolate c:

9 - 2 = 2 - 2  + c

7 = c

<h3>Double-check:</h3>

In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):

f(x) = -2x² + 4x + 7

9 = -2(1)² + 4(1) + 7

9 = -2 + 4 + 7

9 = 9 (True statement).

Therefore, the correct answers are: a = -2, and c = 7.

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6 1⁄3 + 7 1⁄4 – 2 1⁄2 =
Korvikt [17]

Answer:

11 1/12

Step-by-step explanation:

6 1/3 = 19/3

7 1/4 = 29/4

2 1/2 = 5/2

19/3 + 29/4 - 5/2


We must find the LCM of 3, 4, and 2. This happens to be 12

3*4 = 12

4*3 = 12

2*6 = 12

Multiply each fraction by the factor that'll get it to 12.


19/3 * 4/4 = 76/12

29/4 * 3/3 = 87/12

5/2 * 6/6 = 30/12

Now go through the problem


76/12 + 87/12 - 30/12

76 + 87 = 163

163/12 - 30/12

163 - 30 = 133

133/12

Simplify

133/12 = 11.0833... or 11 1/12


Hope this helps.

6 0
3 years ago
Write down all of the prime numbers between 15 and 25.
LUCKY_DIMON [66]

Answer:

17,19,23

that the prime number

8 0
3 years ago
Read 2 more answers
Twice the product of the cube of a and the square of b
arlik [135]

For this case we have to rewrite the given expression algebraically:

the cube of a, is represented as: a ^ 3

the square of b, is represented as:b ^ 2

Thus, the product of both expressions is:

(a ^ 3 * b ^ 2)

And twice the product is represented as:

2 (a ^ 3 * b ^ 2)

Answer:

2 (a ^ 3 * b ^ 2)

6 0
3 years ago
A small school had 60% boys and the rest are girls if the number of boys is 48 what is the total number of boys and girls all to
Flura [38]

Hey there!

When dealing with percent word problems, the word "is" means equals. Let's see what we can do with your problem.

If the small school had 60% boys, it will have 40% girls. The number of boys <em>is</em> 48, which should equal 60% of the total, which we can model below, with t representing the total number of kids. In decimal form, 60% is 0.6.

0.6t=48

We divide both sides by 0.6.

t=80

Therefore, there are 80 total kids at the school.

We can also check our answer below.

BOYS: 0.6(80)= 48

GIRLS: 0.4(80)=32

48+32=80

I hope that this helps!

5 0
3 years ago
I really don't like this site for i need help with my math homework right now and nobody heaven help me yet
Simora [160]
I'm sorry..................
8 0
3 years ago
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