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

y=x^(2)-3x-1
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}-3 x-1$ $\newline$ 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}-3 x-1

\newline

Answer:

y=

Identify coefficients: Identify the coefficients of $x^2$ and $x$ in the quadratic function $y = x^2 - 3x - 1$ . The coefficient of $x^2$ is $1$ , and the coefficient of $x$ is $-3$ .
Find completing square value: Divide the coefficient of $x$ by $2$ and square the result to find the value to complete the square. $\newline$ The coefficient of $x$ is $-3$ , so we divide it by $2$ to get $-\frac{3}{2}$ , and then square $\left(-\frac{3}{2}\right)^2$ to get $\frac{9}{4}$ .
Add/subtract completing square: Add and subtract the value found in Step $2$ inside the equation to complete the square. $\newline$ We add and subtract $\frac{9}{4}$ inside the equation to maintain the equality. $\newline$ $y = x^2 - 3x + \frac{9}{4} - \frac{9}{4} - 1$
Group and combine constants: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 3x + \frac{9}{4}) - \frac{9}{4} - 1$
Factor perfect square trinomial: Factor the perfect square trinomial. $\newline$ The perfect square trinomial $x^2 - 3x + \frac{9}{4}$ factors to $(x - \frac{3}{2})^2$ . $\newline$ $y = (x - \frac{3}{2})^2 - \frac{9}{4} - 1$
Combine constants: Combine the constants to simplify the equation. $\newline$ We combine $-\frac{9}{4}$ and $-1$ (which is the same as $-\frac{4}{4}$ ) to get $-\frac{13}{4}$ . $\newline$ $y = (x - \frac{3}{2})^2 - \frac{13}{4}$

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

\_\_\_\_\_

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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 =

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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

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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 =

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