Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+2 x-4$ $\newline$ Answer: $y=$

View step-by-step help

View step-by-step help

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}+2 x-4

\newline

Answer:

y=

Identify Quadratic Function: To complete the square for the quadratic function $y = x^2 + 2x - 4$ , we first need to focus on the $x^2$ and $2x$ terms. We will add and subtract a certain value to create a perfect square trinomial.
Determine Value to Add/Subtract: The value we need to add and subtract is determined by taking half of the coefficient of $x$ , which is $2$ , and then squaring it. $(2/2)^2 = 1^2 = 1$ . So we will add and subtract $1$ inside the parentheses.
Rewrite Function with Perfect Square Trinomial: We rewrite the function as $y = (x^2 + 2x + 1) - 1 - 4$ . We have added and subtracted $1$ to complete the square.
Factor Perfect Square Trinomial: Now, we can factor the perfect square trinomial as $(x + 1)^2$ . So the function becomes $y = (x + 1)^2 - 1 - 4$ .
Combine Constants: Combine the constants $-1$ and $-4$ to simplify the function. $y = (x + 1)^2 - 5$ .
Convert to Vertex Form: The function is now in vertex form, $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. In this case, the vertex form is $y = (x + 1)^2 - 5$ , with the vertex being $(-1, -5)$ .

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 =

Posted 7 months ago

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

Posted 7 months ago

Question

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

\newline

\cos 90^\circ =

Posted 8 months ago

Related topics

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