Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A parabola opening up or down has vertex $(0,-1)$ and passes through $(12,17)$ . Write its equation in vertex form. $\newline$ Simplify any fractions. $\newline$ ______

View step-by-step help

View step-by-step help

Write a quadratic function from its vertex and another point

Full solution

Q. A parabola opening up or down has vertex

(0,-1)

and passes through

(12,17)

. Write its equation in vertex form.

\newline

Simplify any fractions.

\newline

______

Identify Vertex Values: We have: $\newline$ Vertex: $(0,-1)$ $\newline$ Identify the values of $h$ and $k$ . $\newline$ Vertex is $(0,-1)$ . $\newline$ $h = 0$ $\newline$ $k = -1$
Select Equation: We have: $\newline$ $y = a(x - h)^2 + k$ $\newline$ $h = 0$ and $k = -1$ $\newline$ Select the equation after substituting the values of $h$ and $k$ . $\newline$ Substitute $h = 0$ and $k = -1$ in $y = a(x - h)^2 + k$ . $\newline$ $y = a(x - 0)^2 - 1$ $\newline$ $y = ax^2 - 1$
Find Value of a: We have: $y = ax^2 - 1$
Point: $(12,17)$
Find the value of a.
$y = ax^2 - 1$
$17 = a(12)^2 - 1$
$17 + 1 = a \times 144$
$18 = a \times 144$
$\frac{18}{144} = \frac{(a \times 144)}{144}$
$a = \frac{18}{144}$
$a = \frac{1}{8}$
Write Vertex Form: We found: $\newline$ $a = \frac{1}{8}$ $\newline$ $h = 0$ $\newline$ $k = -1$ $\newline$ Write the equation of a parabola in vertex form. $\newline$ $y = a(x - h)^2 + k$ $\newline$ $y = \frac{1}{8}(x - 0)^2 - 1$ $\newline$ Vertex form: $y = \frac{1}{8}x^2 - 1$

More problems from Write a quadratic function from its vertex 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 1 month 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 1 month 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 1 month 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 1 month ago

Question

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

\newline

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

Posted 1 month 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 1 month 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 2 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 2 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 2 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 2 months ago