mabeloveryShadojel
Answered

"What is the equation, in standard form, of a parabola that contains the following points?


(–2, 18), (0, 2), (4, 42)

Ay = –2x^2 – 2x – 3
By = –3x^2 + 2x – 2
Cy = 3x^2 – 2x + 2
Dy = –2x^2 + 3x + 2"

Verified Answer :

HomertheGenius

We have to use these points to verify which of the equations is correct. 
When we use points in 3rd equation:
( -2, 18) : y= 3 (-2)² - 2 (-2)+2= 12 + 4 + 2 = 18 (true) 
( 0, 2 ) :   y=  3 0² - 2 0 + 2 = 2 (true)
( 4 , 42 ): y= 3 4²- 2 4+ 2 = 48 - 8 + 2 = 42 (true) 
The answer is: C) y=3 x² - 2 x + 2  

The equation in the standard form of the parabola that contains the points \(\left({ - 2,18}\right)\), \(\left({0,2}\right)\) and \(\left({4,42}\right)\) is \(\boxed{y=3{x^2}-2x+2}\).


Further explanation:

The standard form of the parabola is \(y=a{x^2}+bx+c\) .


Given:

The points on the parabola are as follows.

\(\left({-2,18}\right)\), \(\left({0,2}\right)\) and \(\left({4,42}\right)\).


Explanation:

Substitute the point \(\left({-2,18}\right)\) in option A to check whether the point satisfy the equation of the parabola.

\(\begin{aligned}18&=-2{\left({-2}\right)^2}-2\left({-2}\right)-3\\18&=-8+4-3\\18& e-7\\\end{aligned}\)

Therefore, option A is not correct.


Substitute the point \(\left({-2,18}\right)\) in option B to check whether the point satisfy the equation of the parabola.

\(\begin{aligned}18&=-3{\left({-2}\right)^2}+2\left({-2}\right)-2\\18&=-12-4-2\\18& e-18\\\end{aligned}\)

Therefore, option B is not correct.


Substitute the point \(\left({-2,18}\right)\) in option C to check whether the point satisfy the equation of the parabola.

\(\begin{aligned}18&=3{\left({-2}\right)^2}-2\left({-2}\right)+2\\18&=12+4+2\\18&=18\\\end{aligned}\)

Therefore, option C is correct.


Substitute the point \(\left({-2,18}\right)\) in option D to check whether the point satisfy the equation of the parabola.

\(\begin{aligned}18&=-2{\left({-2}\right)^2}+3\left({-2}\right)+2\\18&=-8-6+2\\18& e-12\\\end{aligned}\)

Therefore, option D is not correct.


The equation in the standard form of the parabola that contains the points \(\left({-2,18}\right),\left({0,2}\right)\) and \(\left({4,42}\right)\) is \(\boxed{y=3{x^2}-2x+2}\) .


Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497


Answer details:

Grade: High School

Subject: Mathematics

Chapter: Conic Sections


Keywords: parabola, standard form of the parabola, points, vertices, equation, focus, numbers.

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