Question

Write each function in vertex form. $$ y=-5 x^{2}+12 $$

   Write each function in vertex form.
$$
y=-5 x^{2}+12
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 30

Instant Answer

Solved by Expert Amrita Bhasin

08/08/2019

Step 1

Step 1: The vertex form of a quadratic function is given by $y=a(x-h)^{2}+k$, where $(h,k)$ is the vertex of the parabola. Show more…

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Write each function in vertex form. $$ y=-5 x^{2}+12 $$

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Key Concepts

Vertex Form

The vertex form of a quadratic function is expressed as y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. This form makes it straightforward to identify the maximum or minimum point of the quadratic function as well as its axis of symmetry.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, usually written in the standard form y = ax^2 + bx + c. These functions graph as parabolas and are central in algebra because their characteristics, such as direction, width, vertex, and intercepts, play a key role in various mathematical analyses.

Completing the Square

Completing the square is a method for rewriting a quadratic expression in vertex form. This technique involves modifying the quadratic expression so that it becomes a perfect square trinomial plus or minus a constant, thus revealing the coordinates of the vertex and making graph analysis easier.

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