Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the range of this quadratic function? $\newline$ $y = x^2 - 12x + 32$ $\newline$ Choices: $\newline$ (A) ${y | y \geq -4}$ $\newline$ (B) ${y | y \geq 4}$ $\newline$ (C) ${y | y \geq 6}$ $\newline$ (D)all real numbers

View step-by-step help

View step-by-step help

Domain and range of quadratic functions: equations

Full solution

Q. What is the range of this quadratic function?

\newline

y = x^2 - 12x + 32

\newline

Choices:

\newline

(A)

{y | y \geq -4}

\newline

(B)

{y | y \geq 4}

\newline

(C)

{y | y \geq 6}

\newline

(D)all real numbers

Identify Quadratic Function: Identify the quadratic function. $\newline$ We have the quadratic function $y = x^2 - 12x + 32$ .
Find Vertex x-coordinate: Find the x-coordinate of the vertex. $\newline$ The x-coordinate of the vertex of a quadratic function in the form $y = ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$ . Here, $a = 1$ and $b = -12$ . $\newline$ $x = -(-12)/(2\cdot 1)$ $\newline$ $x = \frac{12}{2}$ $\newline$ $x = 6$
Find Vertex y-coordinate: Find the y-coordinate of the vertex. $\newline$ Substitute $x = 6$ into the quadratic function to find the y-coordinate. $\newline$ $y = (6)^2 - 12(6) + 32$ $\newline$ $y = 36 - 72 + 32$ $\newline$ $y = -36 + 32$ $\newline$ $y = -4$
Determine Parabola Direction: Determine the direction of the parabola. Since $a = 1$ and $a > 0$ , the parabola opens upwards.
Find Range of Function: Find the range of the function. $\newline$ The vertex of the parabola is $(6, -4)$ , and since the parabola opens upwards, the $y$ -values must be greater than or equal to the $y$ -coordinate of the vertex. $\newline$ Range: \{ $y | y \geq -4$ \}

More problems from Domain and range of quadratic functions: equations

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)=

Posted 1 month ago

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 + \_\_\_\_\_

Posted 1 month ago

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

\newline

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