The equation in the standard form of the parabola that contains the points [tex]\left({ - 2,18}\right)[/tex], [tex]\left({0,2}\right)[/tex] and [tex]\left({4,42}\right)[/tex] is [tex]\boxed{y=3{x^2}-2x+2}[/tex].
Further explanation:
The standard form of the parabola is [tex]y=a{x^2}+bx+c[/tex] .
Given:
The points on the parabola are as follows.
[tex]\left({-2,18}\right)[/tex], [tex]\left({0,2}\right)[/tex] and [tex]\left({4,42}\right)[/tex].
Explanation:
Substitute the point [tex]\left({-2,18}\right)[/tex] in option A to check whether the point satisfy the equation of the parabola.
[tex]\begin{aligned}18&=-2{\left({-2}\right)^2}-2\left({-2}\right)-3\\18&=-8+4-3\\18&\ne-7\\\end{aligned}[/tex]
Therefore, option A is not correct.
Substitute the point [tex]\left({-2,18}\right)[/tex] in option B to check whether the point satisfy the equation of the parabola.
[tex]\begin{aligned}18&=-3{\left({-2}\right)^2}+2\left({-2}\right)-2\\18&=-12-4-2\\18&\ne-18\\\end{aligned}[/tex]
Therefore, option B is not correct.
Substitute the point [tex]\left({-2,18}\right)[/tex] in option C to check whether the point satisfy the equation of the parabola.
[tex]\begin{aligned}18&=3{\left({-2}\right)^2}-2\left({-2}\right)+2\\18&=12+4+2\\18&=18\\\end{aligned}[/tex]
Therefore, option C is correct.
Substitute the point [tex]\left({-2,18}\right)[/tex] in option D to check whether the point satisfy the equation of the parabola.
[tex]\begin{aligned}18&=-2{\left({-2}\right)^2}+3\left({-2}\right)+2\\18&=-8-6+2\\18&\ne-12\\\end{aligned}[/tex]
Therefore, option D is not correct.
The equation in the standard form of the parabola that contains the points [tex]\left({-2,18}\right),\left({0,2}\right)[/tex] and [tex]\left({4,42}\right)[/tex] is [tex]\boxed{y=3{x^2}-2x+2}[/tex] .
Learn more:
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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.
