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Complete the square to re-write the quadratic function in vertex form:

y=x^(2)+2x-7
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+2 x-7$ $\newline$ Answer: $y=$

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Write a quadratic function in vertex form

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:

\newline

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

\newline

Answer:

y=

Write Quadratic Equation: Write down the given quadratic equation. $\newline$ We are given the quadratic function $y = x^2 + 2x - 7$ and we need to convert it into vertex form.
Identify Coefficient: Identify the coefficient of $x$ to complete the square. $\newline$ The coefficient of $x$ is $2$ . To complete the square, we need to find $(b/2)^2$ , where $b$ is the coefficient of $x$ . $\newline$ $(\(2\)/\(2\))^\(2\) = \(1\)^\(2\) = \(1\)
Add/Subtract to Complete Square: Add and subtract \((\frac{b}{2})^2\) inside the equation.\(\newline\)We add and subtract \(1\) inside the equation to complete the square.\(\newline\)\(y = x^2 + 2x + 1 - 1 - 7\)
Group and Combine Terms: Group the perfect square trinomial and combine the constants. We group the terms to form a perfect square trinomial and combine the constants \(-1\) and \(-7\). \(y = (x^2 + 2x + 1) - 8\)
Factor Perfect Square Trinomial: Factor the perfect square trinomial.\(\newline\)The perfect square trinomial \(x^2 + 2x + 1\) can be factored into \((x + 1)^2\).\(\newline\)\(y = (x + 1)^2 - 8\)
Write in Vertex Form: Write the equation in vertex form.\(\newline\)The equation is now in vertex form, which is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola.\(\newline\)\(y = (x + 1)^2 - 8\)

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\}

\newline

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

\newline

\text{all real numbers}

Posted 1 month ago

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

Posted 1 month ago

Question

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

\newline

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

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Question

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

Posted 1 month ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

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f(x) = \_\_\_\_\_

Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\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