Question

Rewrite each equation in vertex form. $$ y=x^{2}+4 x+1 $$

   Rewrite each equation in vertex form.
$$
y=x^{2}+4 x+1
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 31

Instant Answer

Solved by Expert Martha Richards

11/25/2019

Step 1

We need to rewrite this equation in vertex form. The vertex form of a quadratic equation is $y=a(x-h)^{2}+k$, where $(h,k)$ is the vertex of the parabola. Show more…

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Rewrite each equation in vertex form. $$ y=x^{2}+4 x+1 $$

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Key Concepts

Vertex Form of a Quadratic

The vertex form of a quadratic function is written as y = a(x – h)² + k, where (h, k) represents the vertex of the parabola. This form makes it easier to identify the vertex and analyze the graph’s transformations, such as horizontal and vertical shifts.

Completing the Square

Completing the square is an algebraic method used to transform a quadratic in standard form into its vertex form. This technique involves adding and subtracting the appropriate constant term to create a perfect square trinomial, thereby simplifying the function to clearly reveal the vertex.

Quadratic Functions

Quadratic functions are second-degree polynomials typically expressed in the form ax² + bx + c. Their graphs are parabolas with a distinct vertex point, and they exhibit features such as axis of symmetry and direction of opening depending on the coefficient a.

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