Graph f(x)=x^2

Solve Math

Algebra

Graph f(x)=x^2

$f (x) = x^{2}$

Find the properties of the given parabola.

Tap for more steps...

Rewrite the equation in vertex form.

Tap for more steps...

Complete the square for $x^{2}$ .

Tap for more steps...

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = 0, c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{0}{2 (1)}$

Cancel the common factor of $0$ and $2$ .

Tap for more steps...

Factor $2$ out of $0$ .

$d = \frac{2 (0)}{2 (1)}$

Cancel the common factors.

Tap for more steps...

Cancel the common factor.

$d = \frac{2 \cdot 0}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{0}{1}$

Divide $0$ by $1$ .

$d = 0$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps...

Simplify each term.

Tap for more steps...

Raising $0$ to any positive power yields $0$ .

$e = 0 - \frac{0}{4 (1)}$

Multiply $4$ by $1$ .

$e = 0 - \frac{0}{4}$

Divide $0$ by $4$ .

$e = 0 - 0$

Multiply $- 1$ by $0$ .

$e = 0 + 0$

Add $0$ and $0$ .

$e = 0$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

$x^{2}$

Set $y$ equal to the new right side.

$y = x^{2}$

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = 1$

$h = 0$

$k = 0$

Since the value of $a$ is positive, the parabola opens up.

Opens Up

Find the vertex $(h, k)$ .

$(0, 0)$

Find $p$ , the distance from the vertex to the focus.

Tap for more steps...

Find the distance from the vertex to a focus of the parabola by using the following formula.

$\frac{1}{4 a}$

Substitute the value of $a$ into the formula.

$\frac{1}{4 \cdot 1}$

Cancel the common factor of $1$ .

Tap for more steps...

Cancel the common factor.

$\frac{1}{4 \cdot 1}$

Rewrite the expression.

$\frac{1}{4}$

Find the focus.

Tap for more steps...

The focus of a parabola can be found by adding $p$ to the y-coordinate $k$ if the parabola opens up or down.

$(h, k + p)$

Substitute the known values of $h$ , $p$ , and $k$ into the formula and simplify.

$(0, \frac{1}{4})$

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

$x = 0$

Find the directrix.

Tap for more steps...

The directrix of a parabola is the horizontal line found by subtracting $p$ from the y-coordinate $k$ of the vertex if the parabola opens up or down.

$y = k - p$

Substitute the known values of $p$ and $k$ into the formula and simplify.

$y = - \frac{1}{4}$

Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

Vertex: $(0, 0)$

Focus: $(0, \frac{1}{4})$

Axis of Symmetry: $x = 0$

Directrix: $y = - \frac{1}{4}$

Direction: Opens Up

Vertex: $(0, 0)$

Focus: $(0, \frac{1}{4})$

Axis of Symmetry: $x = 0$

Directrix: $y = - \frac{1}{4}$

Select a few $x$ values, and plug them into the equation to find the corresponding $y$ values. The $x$ values should be selected around the vertex.

Tap for more steps...

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = {(- 1)}^{2}$

Simplify the result.

Tap for more steps...

Raise $- 1$ to the power of $2$ .

$f (- 1) = 1$

The final answer is $1$ .

$1$

The $y$ value at $x = - 1$ is $1$ .

$y = 1$

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = {(- 2)}^{2}$

Simplify the result.

Tap for more steps...

Raise $- 2$ to the power of $2$ .

$f (- 2) = 4$

The final answer is $4$ .

$4$

The $y$ value at $x = - 2$ is $4$ .

$y = 4$

Replace the variable $x$ with $1$ in the expression.

$f (1) = {(1)}^{2}$

Simplify the result.

Tap for more steps...

One to any power is one.

$f (1) = 1$

The final answer is $1$ .

$1$

The $y$ value at $x = 1$ is $1$ .

$y = 1$

Replace the variable $x$ with $2$ in the expression.

$f (2) = {(2)}^{2}$

Simplify the result.

Tap for more steps...

Raise $2$ to the power of $2$ .

$f (2) = 4$

The final answer is $4$ .

$4$

The $y$ value at $x = 2$ is $4$ .

$y = 4$

Graph the parabola using its properties and the selected points.

$\begin{array}{c} x & y \\ - 2 & 4 \\ - 1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \end{array}$

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex: $(0, 0)$

Focus: $(0, \frac{1}{4})$

Axis of Symmetry: $x = 0$

Directrix: $y = - \frac{1}{4}$

$\begin{array}{c} x & y \\ - 2 & 4 \\ - 1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \end{array}$

Do you know how to Graph f(x)=x^2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	three hundred thirty-nine million three hundred eighty-eight thousand six hundred seventy-two

Interesting facts

339388672 has 1024 divisors, whose sum is 9940807296
The reverse of 339388672 is 276883933
Previous prime number is 7

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 49
Digital Root 4

Name

Name	one billion two hundred forty-four million four hundred fifty-one thousand eight hundred forty-three

Interesting facts

1244451843 has 32 divisors, whose sum is 2731308800
The reverse of 1244451843 is 3481544421
Previous prime number is 9

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 36
Digital Root 9

Name

Name	one billion six hundred three million eight hundred sixty thousand ninety-six

Interesting facts

1603860096 has 2048 divisors, whose sum is 37713677760
The reverse of 1603860096 is 6900683061
Previous prime number is 137

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 39
Digital Root 3

Simplify square root of 25

Evaluate cube root of 72

Solve Using the Quadratic Formula 2x^2-7x=1

Evaluate 45/3

Solve Using the Quadratic Formula 3x^2+2x-3=0