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natita [175]
3 years ago
6

Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the gi

ven point. (Let x be the independent variable and y be the dependent variable.)
Vertex: (−3, 4); point: (0, 13)
Mathematics
2 answers:
maks197457 [2]3 years ago
6 0

Answer:

The formula for this quadratic function is x*2 +6x+13

Step-by-step explanation:

If we have the vertex and one point of a parabola it is possible to find the quadratic function by the use of this

y= a (x-h)*2 + K

Quadratic function looks like this

y= ax*2 + bx + c

So let's find the a

y= a (x-h)*2 + K where

y is 13, x is 0, h is -3 and K is 4

13= a (0-(-3))*2 +4

13=9a +4

9=9a

9/9=a

1=a

The quadratic function will be

y= 1(x+3)*2 + 4

Let's get the classic form

(x+3)*2 = (x+3)(x+3)

(x*2+3x+3x+9)

x*2 +6x+13

f(0) = 13

Crazy boy [7]3 years ago
6 0

Answer:

y = x^2 + 6x + 13.

Step-by-step explanation:

The general vertex  form is

y = = a(x - b)^2 + c   where a is a constant and (b, c) is the vertex.

So as the vertex is (-3, 4) we have:

y =  a(x - -3)^2 + 4

y = a(x + 3)^2 + 4

Now we find the value of a by substituting the point (0, 13)

13 = a (0 + 3)^2 + 4

13 = 9a + 4

9a = 13-4 = 9

a = 1.

So our equation is y = (x + 3)^2 + 4

Converting to Standard Form:

y = x^2 + 6x + 9 + 4

y = x^2 + 6x + 13.

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Answer:

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Step-by-step explanation:

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A line with a slope of 5 passes through the point (1,8). What is its equation in
Eduardwww [97]

Answer:

Step-by-step explanation:

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An orange costs $2 while a banana costs $1.5. How many oranges and bananas do you have to buy such that the total cost would equal to $20. You bought a total of 12 fruits.

First, you have to introduce variables. Let 'x' be the number of oranges and 'y' be the number of bananas. One equation you can get from here is knowing the amount of total cost: 2x + 1.5y = 20. Then, the other equation would be knowing the amount of fruits: x+y=12. You have two unknowns and two equations. Hence, you can solve the problem. Solving them simultaneously, you would get that x=4 and y=8.
4 0
3 years ago
Can someone help me i keep getting different answer!!
spayn [35]

Answer:

The second option: 3 (6 - 5n)/20n

Step-by-step explanation:

Make sure all fractions have a common denominator:

Step 1. Find a common multiple between all three denominators

5, 4, and 10 all have a common multiple of 20. Proof: 5 × 4 = 20, 4 × 5 = 20, and 10 × 2 = 20

Step 2. Multiply the denominators to get to 20. Whatever you do to the bottom (denominator) must be done to the top (numerator).

1/5n × 4/4 = 4/20n

3/4 × 5n/5n = 15n/20n

7/10n × 2/2 = 14/20n

Your fractions now all have a common denominator of 20n.

Rewrite the equation using the new fractions:

4/20n - 15n/20n + 14/20n

Only focus on adding/subtracting the numerators; the denominators will stay the same: 20n.

(4 - 15n + 14)/20n

Combine like terms:

(18 - 15n)/20n

Factor out any numbers possible:

3(6 - 5n)/20n

Note* 3 go into both 18 and 15, which allows us to factor 3 out. 18 ÷ 3 = 6 and 15 ÷ 3 = 5, giving us our new numbers inside the parentheses.

6 0
3 years ago
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