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 parabola that passes through the points (−1,12(-1,12), (−2,0(-2,0), and (1,0(1,0). 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.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. Write the equation of the parabola that passes through the points (−1,12(-1,12), (−2,0(-2,0), and (1,0(1,0). 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.
  1. Identify x-intercepts: We have the points (−1,12)(-1,12), (−2,0)(-2,0), and (1,0)(1,0). The points (−2,0)(-2,0) and (1,0)(1,0) are the x-intercepts of the parabola, so they give us the values of pp and qq directly. Therefore, p=−2p = -2 and q=1q = 1.
  2. Write parabola equation: Using the values of pp and qq, we can write the equation of the parabola in the form y=a(x−p)(x−q)y = a(x - p)(x - q). Substituting −2-2 for pp and 11 for qq, we get y=a(x+2)(x−1)y = a(x + 2)(x - 1).
  3. Find value of a: Now we need to find the value of aa. We can use the point (−1,12)(-1,12) to do this. Substituting −1-1 for xx and 1212 for yy in the equation y=a(x+2)(x−1)y = a(x + 2)(x - 1), we get 12=a(−1+2)(−1−1)12 = a(-1 + 2)(-1 - 1).
  4. Solve for aa: Solving the equation 12=a(1)(−2)12 = a(1)(-2), we find that 12=−2a12 = -2a, which means a=−6a = -6.
  5. Final equation of parabola: Now that we have found a=−6a = -6, we can write the final equation of the parabola. Substituting −6-6 for aa, −2-2 for pp, and 11 for qq in the equation y=a(x−p)(x−q)y = a(x - p)(x - q), we get y=−6(x+2)(x−1)y = -6(x + 2)(x - 1).

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 8 months 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 7 months 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 5 months 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 5 months 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 5 months 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 5 months 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 5 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 4 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 4 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 5 months ago

View all (106)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant