Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the minimum value of the function
f(x)=2x^(2)-11.4 x+21 to the nearest hundredth.
Answer:

Find the minimum value of the function $f(x)=2 x^{2}-11.4 x+21$ to the nearest hundredth. $\newline$ Answer:

View step-by-step help

View step-by-step help

Find trigonometric functions using a calculator

Full solution

Q. Find the minimum value of the function

f(x)=2 x^{2}-11.4 x+21

to the nearest hundredth.

\newline

Answer:

Find Vertex Form: To find the minimum value of the quadratic function $f(x) = 2x^2 - 11.4x + 21$ , we need to find the vertex of the parabola. The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. Since the coefficient of $x^2$ is positive, the parabola opens upwards, and the vertex represents the minimum point.
Calculate x-coordinate: The x-coordinate of the vertex $h$ can be found using the formula $h = -\frac{b}{2a}$ , where $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $x$ in the standard form of the quadratic function. For the given function, $a = 2$ and $b = -11.4$ .
Calculate y-coordinate: Let's calculate the x-coordinate of the vertex: $\newline$ $h = -(-11.4) / (2 \times 2) = 11.4 / 4 = 2.85$
Substitute into Function: Now that we have the $x$ -coordinate of the vertex, we can find the $y$ -coordinate ( $k$ ) by substituting $h$ back into the original function: $\newline$ $f(2.85) = 2(2.85)^2 - 11.4(2.85) + 21$
Calculate Minimum Value: Let's perform the calculation: $\newline$ $f(2.85) = 2(8.1225) - 32.49 + 21$ $\newline$ $f(2.85) = 16.245 - 32.49 + 21$ $\newline$ $f(2.85) = -16.245 + 21$ $\newline$ $f(2.85) = 4.755$
Calculate Minimum Value: Let's perform the calculation: $\newline$ $f(2.85) = 2(8.1225) - 32.49 + 21$ $\newline$ $f(2.85) = 16.245 - 32.49 + 21$ $\newline$ $f(2.85) = -16.245 + 21$ $\newline$ $f(2.85) = 4.755$ The minimum value of the function to the nearest hundredth is therefore $4.76$ , as we round $4.755$ to the nearest hundredth.

More problems from Find trigonometric functions using a calculator

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 9 months ago

Related topics

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