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The equation of a parabola is $y = x^2 + 4x + 1$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 + 4x + 1

. Write the equation in vertex form.

\newline

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

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the Square: Complete the square to transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 + 4x + 1$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 + 4x$ . $\newline$ The value needed is $(4/2)^2 = 2^2 = 4$ . We will add and subtract this value inside the equation.
Add and Subtract Value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 + 4x + 1$ $\newline$ $y = x^2 + 4x + 4 - 4 + 1$ $\newline$ We added and subtracted $4$ to create a perfect square trinomial without changing the value of the equation.
Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 + 4x + 4) - 4 + 1$ $\newline$ $y = (x + 2)^2 - 3$ $\newline$ Now the equation is in vertex form, where $(x + 2)^2$ is the perfect square trinomial and $-3$ is the combination of the constants.

More problems from Write a quadratic function in vertex form

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 1 month ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

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Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

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\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

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Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

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Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

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h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

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Question

Write a quadratic function with zeros

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\newline

Write your answer using the variable

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Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

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\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 2 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 2 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 2 months ago