Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the equation of the axis of symmetry for the parabola $y = x^2 + 6x + \frac{71}{10}$ . $\newline$ Simplify any numbers and write them as proper fractions, improper fractions, or integers. $\newline$ $\_\_$

View step-by-step help

View step-by-step help

Characteristics of quadratic functions: equations

Full solution

Q. Find the equation of the axis of symmetry for the parabola

y = x^2 + 6x + \frac{71}{10}

.

\newline

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

\newline

\_\_

Identify Coefficients: Identify the coefficients of the quadratic equation. $\newline$ The quadratic equation is given in the form $y = ax^2 + bx + c$ . For the parabola $y = x^2 + 6x + \frac{71}{10}$ , we can identify the coefficients as follows: $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = 6$ (coefficient of $x$ ) $\newline$ $c = \frac{71}{10}$ (constant term)
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry. $\newline$ The axis of symmetry for a parabola in the form $y = ax^2 + bx + c$ is given by the formula $x = -\frac{b}{2a}$ . We will substitute the values of $a$ and $b$ into this formula to find the axis of symmetry.
Substitute Values into Formula: Substitute the values of $a$ and $b$ into the formula. $\newline$ Using $a = 1$ and $b = 6$ , we get: $\newline$ $x = -\frac{b}{2a}$ $\newline$ $x = -\frac{6}{2 \times 1}$ $\newline$ $x = -\frac{6}{2}$ $\newline$ $x = -3$ $\newline$ The equation of the axis of symmetry is $x = -3$ .

More problems from Characteristics of quadratic functions: equations

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