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:

Find the equation of the axis of symmetry for the parabola y=x2+xy = x^2 + x. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____\_\_\_\_\_

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

Full solution

Q. Find the equation of the axis of symmetry for the parabola y=x2+xy = x^2 + x. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____\_\_\_\_\_
  1. Identify Coefficients: Identify the coefficients of the quadratic equation.\newlineThe given parabola is y=x2+xy = x^2 + x. This can be compared to the standard form of a quadratic equation, which is y=ax2+bx+cy = ax^2 + bx + c. Here, a=1a = 1, b=1b = 1, and cc is not given because it is 00.
  2. Use Axis of Symmetry Formula: Use the formula for the axis of symmetry.\newlineThe axis of symmetry for a parabola given by y=ax2+bx+cy = ax^2 + bx + c is x=−b2ax = -\frac{b}{2a}. We will substitute the values of aa and bb into this formula to find the axis of symmetry.
  3. Substitute Values: Substitute the values of aa and bb into the formula.\newlinea=1a = 1 and b=1b = 1, so the axis of symmetry is x=−1(2⋅1)=−12x = -\frac{1}{(2 \cdot 1)} = -\frac{1}{2}.
  4. Write Equation: Write the equation of the axis of symmetry.\newlineThe axis of symmetry is a vertical line, so its equation is x=constantx = \text{constant}. In this case, the constant is −12-\frac{1}{2}. Therefore, the equation of the axis of symmetry is x=−12x = -\frac{1}{2}.

More problems from Characteristics 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 (132)