The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].
Further Explanation:
The standard form of the parabola is shown below.
[tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]
Here, the parabola has vertex at [tex]\left({h,k}\right)[/tex] and has the symmetry parallel to x-axis and it opens left.
Given:
The quadratic function is [tex]y=3{\left({x+2}\right)^2}-3[/tex].
Calculation:
Compare the [tex]y=3{\left({x+2}\right)^2}-3[/tex] with the general equation of the parabola [tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]
.
The value [tex]a[/tex] is [tex]3[/tex], the value of [tex]h[/tex] is [tex]-2[/tex] and the value of [tex]k[/tex] is [tex]-3[/tex].
Therefore, the vertex of the parabola is [tex]\left({-2,-3}\right)[/tex].
The function is symmetric about [tex]x=-2[/tex].
The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear https://brainly.com/question/4165000
3. Learn more about binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Conic sections
Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola,
