Put the quadratic into vertex form and state the coordinates of the vertex. y=x^(2)+4x-21 Vertex Form: y= Vertex: (◻,◻)

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete the Square: Complete the square to transform the given quadratic equation into vertex form. Given equation: y = x^2 + 4x - 21 To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the x^2 and 4x terms.Calculate Value: Calculate the value needed to complete the square. The coefficient of x is 4. Half of this coefficient is 2, and squaring this value gives us 4. We will add and subtract 4 to complete the square.Rewrite Equation: Rewrite the equation by adding and subtracting the value found in Step 3 inside the parentheses. y = x^2 + 4x + 4 - 4 - 21 y = (x^2 + 4x + 4) - 25 Now, the expression in the parentheses is a perfect square trinomial.Factor and Simplify: Factor the perfect square trinomial and simplify the equation. y = (x + 2)^2 - 25 This is the vertex form of the given quadratic equation.Identify Vertex: Identify the vertex of the parabola from the vertex form. The vertex form of the equation is y = (x + 2)^2 - 25, so the vertex (h, k) is (-2, -25).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Put the quadratic into vertex form and state the coordinates of the vertex.

y=x^(2)+4x-21
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}+4 x-21$ $\newline$ Vertex Form: $y=$ $\newline$ Vertex: $(\square, \square)$

View step-by-step help

Home

Math Problems

Algebra 2

Convert equations of parabolas from general to vertex form

Full solution

Q. Put the quadratic into vertex form and state the coordinates of the vertex.

\newline

y=x^{2}+4 x-21

\newline

Vertex Form:

y=

\newline

Vertex:

(\square, \square)

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the Square: Complete the square to transform the given quadratic equation into vertex form. $\newline$ Given equation: $y = x^2 + 4x - 21$ $\newline$ To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the $x^2$ and $4x$ terms.
Calculate Value: Calculate the value needed to complete the square. $\newline$ The coefficient of $x$ is $4$ . Half of this coefficient is $2$ , and squaring this value gives us $4$ . We will add and subtract $4$ to complete the square.
Rewrite Equation: Rewrite the equation by adding and subtracting the value found in Step $3$ inside the parentheses. $\newline$ $y = x^2 + 4x + 4 - 4 - 21$ $\newline$ $y = (x^2 + 4x + 4) - 25$ $\newline$ Now, the expression in the parentheses is a perfect square trinomial.
Factor and Simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x + 2)^2 - 25$ $\newline$ This is the vertex form of the given quadratic equation.
Identify Vertex: Identify the vertex of the parabola from the vertex form. $\newline$ The vertex form of the equation is $y = (x + 2)^2 - 25$ , so the vertex $(h, k)$ is $(-2, -25)$ .