Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the range of this quadratic function?\newliney=x2−10x+21y = x^2 - 10x + 21\newlineChoices:\newline(A)y∣y≥5{y | y \geq 5}\newline(B)y∣y≤5{y | y \leq 5}\newline(C)y∣y≥−4{y | y \geq -4}\newline(D)all real numbers

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Domain and range of quadratic functions: equationsright chevron icon

Full solution

Q. What is the range of this quadratic function?\newliney=x2−10x+21y = x^2 - 10x + 21\newlineChoices:\newline(A)y∣y≥5{y | y \geq 5}\newline(B)y∣y≤5{y | y \leq 5}\newline(C)y∣y≥−4{y | y \geq -4}\newline(D)all real numbers
  1. Identify Quadratic Function: Identify the quadratic function.\newlineWe are given the quadratic function y=x2−10x+21y = x^2 - 10x + 21.
  2. Find Vertex: Find the xx-coordinate of the vertex.\newlineTo find the vertex of the parabola, we use the formula x=−b2ax = -\frac{b}{2a}, where aa is the coefficient of x2x^2 and bb is the coefficient of xx. In this case, a=1a = 1 and b=−10b = -10.\newlinex=−−102⋅1x = -\frac{-10}{2 \cdot 1}\newlinex=102x = \frac{10}{2}\newlinex=−b2ax = -\frac{b}{2a}00
  3. Find Y-Coordinate: Find the y-coordinate of the vertex.\newlineSubstitute x=5x = 5 into the quadratic function to find the y-coordinate of the vertex.\newliney=(5)2−10(5)+21y = (5)^2 - 10(5) + 21\newliney=25−50+21y = 25 - 50 + 21\newliney=−25+21y = -25 + 21\newliney=−4y = -4
  4. Determine Parabola Direction: Determine the direction of the parabola. Since the coefficient of x2x^2 (a=1a = 1) is positive, the parabola opens upwards.
  5. Find Range: Find the range of the function.\newlineThe vertex of the parabola is (5,−4)(5, -4), and since the parabola opens upwards, the yy-values will be greater than or equal to the yy-coordinate of the vertex.\newlineRange: \{y∣y≥−4y | y \geq -4\}
  6. Match Range with Choices: Match the range with the given choices.\newlineThe correct range is not listed in the choices provided. There seems to be an error in the choices, as none of them match the calculated range of y∣y≥−4{y | y \geq -4}.

More problems from Domain and range of quadratic functions: equations

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 1 month ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

View all (34)