Question

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

Answer 1

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  

Answer 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.

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

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.

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

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.

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

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 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 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.