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

y=x^(2)-8x+5
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}-8 x+5$ $\newline$ Answer: $y=$

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Csc, sec, and cot of special angles

Full solution

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

\newline

y=x^{2}-8 x+5

\newline

Answer:

y=

Identify Perfect Square Trinomial: To complete the square, we need to find a value that, when added and subtracted to the quadratic expression, forms a perfect square trinomial. The coefficient of $x^2$ is $1$ , so we only need to focus on the $x$ -term, which is $-8x$ . We take half of the coefficient of $x$ , which is $-8/2 = -4$ , and square it to get $16$ . This is the value we will add and subtract inside the parentheses.
Add and Subtract Value: We rewrite the quadratic function by adding and subtracting $16$ inside the parentheses, and then we will move the constant term outside the parentheses. $\newline$ $y = x^2 - 8x + 16 - 16 + 5$
Group Trinomial and Constants: Now we group the perfect square trinomial and the constants separately. $\newline$ $y = (x^2 - 8x + 16) - 16 + 5$
Factor Perfect Square Trinomial: The perfect square trinomial $(x^2 - 8x + 16)$ can be factored into $(x - 4)^2$ , and we combine the constants $-16$ and $+5$ . $\newline$ $y = (x - 4)^2 - 11$

More problems from Csc, sec, and cot of special angles

Question

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\cos(\theta) = -1

\newline

\underline{\hspace{2em}}^\circ

Posted 7 months ago

Question

Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

\newline

\_\_\_\_\_

Posted 7 months ago

Question

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

\newline

\cos 35^\circ =

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Question

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

\newline

\_\_\_\_\,^\circ

Posted 8 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cot 30^\circ =

Posted 7 months ago

Question

The terminal side of an angle

\theta

in standard position intersects the unit circle at

(\frac{84}{85}, \frac{13}{85})

\cos(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

Posted 7 months ago

Question

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

^\circ

\newline

Posted 8 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

Posted 8 months ago

Question

\theta

is an acute angle. Find the value of

\theta

\newline

\sec(\theta) = \sqrt{2}

\newline

\theta =

\degree

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Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cos 90^\circ =

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Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant