Resources

Resources

Bytelearn - cat image with glasses

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

View step-by-step help

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 $(-2, -25)$ .

More problems from Convert equations of parabolas from general to vertex form

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

Posted 1 month ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 2 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 2 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 2 months ago

Question

What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

Posted 2 months ago

Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Posted 2 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 1 month ago

Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

(0,4)

and the radius is

1

\newline

(D) The center is

(0,-4)

and the radius is

1

Posted 4 months ago

Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

Posted 4 months ago

Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

-coordinate of the vertex

Posted 4 months ago