Question

What is the vertex form of the equation?

y = x2 + 4x – 3

A. y = (x – 2)2 – 7
B. y = (x + 2)2 – 7
C. y = (x – 2)2 + 7
D. y = (x + 2)2 + 7

Answer 1

We need to write the equation in its vertex form so we have to know the general equation for the vertex form. It is written as:

y = (x - h)^2 + k

where h and k represents the point of the vertex.

We go as follows:

y = (x^2 + 4x) – 3 
y +4= (x^2 + 4x+4) – 3 
y = (x + 2)^2 - 7

Therefore, the correct answer from the choices is option B.

Answer 2

The vertex form of the equation $x^{2}+4x-3$ is $\fbox{\begin{minispace}\\ \math (x+2)^{2} -7\end{minispace}}$, that is $\fbox{\begin{minispace}\\option B\end{minispace}}$.

Step-by-step explanation:

A quadratic equation is a two degree equation that has the standard form $ax^{2}+bx+c$.

The degree of the given equation $x^{2}+4x-3$ is $2$ therefore it is a quadratic equation.

Every quadratic equation represents a parabola so the given equation also represents a parabolic function.

The standard form of equation of a parabola is written as shown below.

$\fbox{\begin{minispace}\\ \math a(x-h)^{2}+k\end{minispace}}$

Here, the value of $a$ represents whether the parabola is upwards or downward and the point $(h,k)$ is the vertex of the parabola.

Therefore, the above equation form is known as the vertex form of the equation.

To transform any quadratic equation into its vertex form, we use completing the square method.

Firstly, if the coefficient of $x^{2}$ is other than $1$ then divide the complete equation by that coefficient.

Here, the coefficient of $x^{2}$ is $1$ so the first step is not required.

Now, add a value and subtract the same value such that it forms a perfect square.

For a standard quadratic equation $ax^{2}+bx+c$, the value that is added and subtracted in the expression is calculated as $\left(\dfrac{b}{2a}\right)^{2}$.

Hence, add and subtract $4$ to the equation and simplify as shown below.

$\begin{aligned}x^{2}+4x-3&=x^{2}+4x-3+4-4\\&=x^{2}+4x+4-3-4\\&=(x+2)^{2}-7\end{aligned}$

Therefore, the vertex form of the equation $x^{2}+4x-3$ is $\fbox{\begin{minispace}\\ \math (x+2)^{2} -7\end{minispace}}$.

Learn more:

1. General form of equation of a circle https://brainly.com/question/1506955

2. Domain and range of a function https://brainly.com/question/3412497

3. Coordinate geometry https://brainly.com/question/7437053

Answer details

Grade: Middle school

Subject: Mathematics  

Chapter: Quadratic equation

Keywords: equation, vertex form, quadratic equation, parabola, vertex, coefficients, add, subtract, divide, standard form, simplify, completing the square, vertex point, degree.