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 (1,0)(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______

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 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______
  1. Identify x-intercepts: We are given three points through which the parabola passes: (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,–16). The points (1,0)(1,0) and (2,0)(2,0) are the x-intercepts of the parabola, which means they correspond to the values of pp and qq in the equation y=a(x–p)(x–q)y = a(x – p)(x – q). Therefore, we can immediately identify p=1p = 1 and q=2q = 2.
  2. Write parabola equation: Now that we have pp and qq, we can write the equation of the parabola as y=a(x–1)(x–2)y = a(x – 1)(x – 2). However, we still need to find the value of the coefficient aa. To do this, we will use the third point (3,–16)(3, –16) by substituting xx with 33 and yy with –16–16 in the equation and solving for aa.
  3. Substitute third point: Substituting the point (3,−16)(3, -16) into the equation gives us −16=a(3−1)(3−2)-16 = a(3 - 1)(3 - 2). Simplifying the right side of the equation, we get −16=a(2)(1)-16 = a(2)(1), which simplifies further to −16=2a-16 = 2a. Dividing both sides by 22, we find that a=−16/2=−8a = -16 / 2 = -8.
  4. Solve for coefficient aa: Having found a=−8a = -8, we can now write the complete equation of the parabola. Substituting aa, pp, and qq into y=a(x−p)(x−q)y = a(x - p)(x - q) gives us the final equation y=−8(x−1)(x−2)y = -8(x - 1)(x - 2).

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 5 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 5 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 2 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 2 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 2 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 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

Question
Apply the distributive property to factor out the greatest common factor.\newline25p+50q=25 p+50 q=\newline□ \square
Get tutor helpright-arrow

Posted 17 hours ago

View all (218)

Related topics

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