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+4x+4y = x^2 + 4x + 4\newlineChoices:\newline(A)y∣y≥−2{y | y \geq -2}\newline(B)y∣y≤0{y | y \leq 0}\newline(C)y∣y≥0{y | y \geq 0}\newline(D)all real numbers

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Domain and range of quadratic functions: equationsright chevron icon

Full solution

Q. What is the range of this quadratic function?\newliney=x2+4x+4y = x^2 + 4x + 4\newlineChoices:\newline(A)y∣y≥−2{y | y \geq -2}\newline(B)y∣y≤0{y | y \leq 0}\newline(C)y∣y≥0{y | y \geq 0}\newline(D)all real numbers
  1. Identify Quadratic Function: Identify the quadratic function and its coefficients.\newlineThe given quadratic function is y=x2+4x+4y = x^2 + 4x + 4. Here, the coefficients are a=1a = 1, b=4b = 4, and c=4c = 4.
  2. Find Vertex x-coordinate: Find the x-coordinate of the vertex of the parabola.\newlineThe x-coordinate of the vertex can be found using the formula x=−b2ax = -\frac{b}{2a}. Substituting the values of aa and bb, we get:\newlinex=−42×1x = -\frac{4}{2 \times 1}\newlinex=−42x = -\frac{4}{2}\newlinex=−2x = -2
  3. Find Vertex y-coordinate: Find the y-coordinate of the vertex by substituting the x-coordinate into the original equation.\newlineSubstitute x=−2x = -2 into y=x2+4x+4y = x^2 + 4x + 4 to find the y-coordinate of the vertex:\newliney=(−2)2+4(−2)+4y = (-2)^2 + 4(-2) + 4\newliney=4−8+4y = 4 - 8 + 4\newliney=0y = 0
  4. Determine Parabola Direction: Determine the direction in which the parabola opens.\newlineSince the coefficient a=1a = 1 is positive, the parabola opens upwards.
  5. Find Range: Find the range of the quadratic function.\newlineThe vertex of the parabola is (−2,0)(-2, 0), and since the parabola opens upwards, the range of the function is all yy-values greater than or equal to the yy-coordinate of the vertex.\newlineRange: \{y∣y≥0y | y \geq 0\}

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 (112)