Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the equation of the parabola that passes through the points $(1,0)$ , $(6,0)$ , and $(7,30)$ . Write your answer in the form $y = a(x - p)(x - q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions.

View step-by-step help

View step-by-step help

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

Full solution

Q. Write the equation of the parabola that passes through the points

(1,0)

,

(6,0)

, and

(7,30)

. Write your answer in the form

y = a(x - p)(x - q)

, where

a

,

p

, and

q

are integers, decimals, or simplified fractions.

Identify x-intercepts: We have: $\newline$ Points: $(1,0)$ , $(6,0)$ and $(7,30)$ $\newline$ Identify x-intercepts from the given points. $\newline$ The x-intercepts are the x-values of the points where the y-values are zero. $\newline$ x-intercepts: $1$ , $6$
Simplify using x-intercepts: We have: $\newline$ $p = 1$ $\newline$ $q = 6$ $\newline$ Simplify $y = a(x - p)(x - q)$ using x-intercepts. $\newline$ $y = a(x - p)(x - q)$ $\newline$ $y = a(x - 1)(x - 6)$
Simplify with given point: We have: $\newline$ $y = a(x - 1)(x - 6)$ $\newline$ Point: $(7,30)$ $\newline$ Simplify $y = a(x - 1)(x - 6)$ . $\newline$ $y = a(x - 1)(x - 6)$ $\newline$ $30 = a(7 - 1)(7 - 6)$ $\newline$ $30 = a(6)(1)$ $\newline$ $30 = 6a$
Solve for $a$ : We have: $\newline$ $30 = 6a$ $\newline$ Solve for $a$ . $\newline$ $30 = 6a$ $\newline$ $\frac{30}{6} = \frac{6a}{6}$ $\newline$ $a = 5$
Write parabola equation: We have: $\newline$ $a = 5$ $\newline$ $p = 1$ $\newline$ $q = 6$ $\newline$ Write the equation of the parabola in the form $y = a(x - p)(x - q)$ . $\newline$ $y = a(x - 1)(x - 6)$ $\newline$ $y = 5(x - 1)(x - 6)$

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

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 8 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 7 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 5 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 5 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 5 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 5 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 5 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 4 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant