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 of the following parabola using graphing technology.

y=x^(2)-4x-2
Answer:

Find the equation of the axis of symmetry of the following parabola using graphing technology. $\newline$ $y=x^{2}-4 x-2$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Find the axis of symmetry of a parabola

Full solution

Q. Find the equation of the axis of symmetry of the following parabola using graphing technology.

\newline

y=x^{2}-4 x-2

\newline

Answer:

Find Vertex: The equation of the parabola is given by $y = x^2 - 4x - 2$ . To find the axis of symmetry, we need to find the $x$ -coordinate of the vertex of the parabola. The axis of symmetry can be found using the formula $x = -\frac{b}{2a}$ , where $a$ and $b$ are the coefficients from the quadratic equation in the form $y = ax^2 + bx + c$ .
Calculate Coefficients: In our equation, $y = x^2 - 4x - 2$ , the coefficient $a$ is $1$ and the coefficient $b$ is $-4$ . We will substitute these values into the formula to find the $x$ -coordinate of the vertex.
Substitute into Formula: Using the formula $x = -\frac{b}{2a}$ , we substitute $a = 1$ and $b = -4$ to get $x = -\frac{(-4)}{2\cdot 1} = \frac{4}{2} = 2$ .
Determine Axis of Symmetry: The $x$ -coordinate of the vertex is $2$ , which means the axis of symmetry is the vertical line that passes through this $x$ -coordinate. Therefore, the equation of the axis of symmetry is $x = 2$ .

More problems from Find the axis of symmetry of a parabola

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

Posted 1 month ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 2 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 2 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 2 months ago

Question

What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

Posted 2 months ago

Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Posted 2 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 1 month ago

Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

(0,4)

and the radius is

1

\newline

(D) The center is

(0,-4)

and the radius is

1

Posted 4 months ago

Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

Posted 4 months ago

Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

-coordinate of the vertex

Posted 4 months ago