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sleet_krkn [62]
3 years ago
13

How do I solve this? Thank you!

Mathematics
1 answer:
Marat540 [252]3 years ago
3 0
Probably A but not sure
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A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)
LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

  • You must have 3 points lie on the parabola
  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
  • Solve the system of equation to find them

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

6 0
3 years ago
Read 2 more answers
7<br> Tuesday<br> Find the Greatest Common<br> Factor of 16 and 28:
Anna35 [415]

Answer:

The answer is 4.

Step-by-step explanation:

1. find the factors of 16(1,2,4,4,8,16) and of 28(1,2,4,7,14,28)

2. find the highest factor of the two Factored #.(4)

8 0
3 years ago
NEED HELP NOW! SOLVE THE INEQUALITY: -r/3 ≤ 6
larisa [96]

Answer:

r\geq -18

Step-by-step explanation:

\frac{-r}{3} \leq 6\\\rule{150}{0.5}\\(\frac{-r}{3})*3\leq 6*3\\\\-r \leq 18\\\\\frac{-r \leq 18}{-1}\\\\\boxed{ r\geq -18}

Hope this helps!

5 0
3 years ago
What is 3 1/2 - 2 5/7 and show the work
Hunter-Best [27]
3 \frac{1}{2}  -2 \frac{5}{7} = \frac{(3\cdot2)+1}{2} -  \frac{(2\cdot7)+5}{7} =  \frac{7}{2} -  \frac{19}{7} \\\\= \frac{7\times 7}{2\times 7} -  \frac{19\times 2}{7\times 2} =  \frac{49}{14} - \frac{38}{14} \\\\= \frac{49-38}{14} =\boxed{\bf{\frac{11}{14}}}
6 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%7B75%7D%5E%7B2%7D%20%2B%2025%20-%20750" id="TexFormula1" title=" {75}^{2} + 25 - 750" alt=
frez [133]
your answer is 4900
3 0
3 years ago
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