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:

Write the equation of the quadratic function given the three points on the function. Write the equation in standard form f(x)=ax2+bx+cf(x) = ax^2 + bx + c. (0,−12)(0, -12), (1,−9)(1, -9), (−2,−36)(-2, -36)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. Write the equation of the quadratic function given the three points on the function. Write the equation in standard form f(x)=ax2+bx+cf(x) = ax^2 + bx + c. (0,−12)(0, -12), (1,−9)(1, -9), (−2,−36)(-2, -36)
  1. Find cc: Plug in the first point (0,−12)(0, -12) into the standard form equation to find cc.f(x)=ax2+bx+cf(x) = ax^2 + bx + c−12=a(0)2+b(0)+c-12 = a(0)^2 + b(0) + cc=−12c = -12
  2. Relationship between aa and bb: Plug in the second point (1,−9)(1, -9) into the standard form equation to find a relationship between aa and bb.
    −9=a(1)2+b(1)+c-9 = a(1)^2 + b(1) + c
    −9=a+b−12-9 = a + b - 12
    a+b=3a + b = 3
  3. Another relationship between a and b: Plug in the third point (−2,−36)(-2, -36) into the standard form equation to find another relationship between a and b.\newline−36=a(−2)2+b(−2)+c-36 = a(-2)^2 + b(-2) + c\newline−36=4a−2b−12-36 = 4a - 2b - 12\newline4a−2b=−244a - 2b = -24
  4. Solve system of equations: Solve the system of equations from the second and third steps to find aa and bb.a+b=3a + b = 34a−2b=−244a - 2b = -24Multiply the first equation by 22 and add to the second equation.2a+2b=62a + 2b = 64a−2b=−244a - 2b = -246a=−186a = -18a=−3a = -3
  5. Find bb: Substitute a=−3a = -3 into the first equation to find bb.\newline−3+b=3-3 + b = 3\newlineb=6b = 6
  6. Write final equation: Write the final equation using the values of aa, bb, and cc.f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=−3x2+6x−12f(x) = -3x^2 + 6x - 12

More problems from Write a quadratic function from its x-intercepts and another point

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 (141)