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Examples

(0, 0)

$(0, 0)$ ,

(1, 1)

$(1, 1)$

Step 1

The general equation of a parabola with vertex

(h, k)

$(h, k)$ is

y = a {(x - h)}^{2} + k

$y = a {(x - h)}^{2} + k$ . In this case we have

(0, 0)

$(0, 0)$ as the vertex

(h, k)

$(h, k)$ and

(1, 1)

$(1, 1)$ is a point

(x, y)

$(x, y)$ on the parabola. To find

a

$a$ , substitute the two points in

y = a {(x - h)}^{2} + k

$y = a {(x - h)}^{2} + k$ .

1 = a {(1 - (0))}^{2} + 0

$1 = a {(1 - (0))}^{2} + 0$

Step 2

Using

1 = a {(1 - (0))}^{2} + 0

$1 = a {(1 - (0))}^{2} + 0$ to solve for

a

$a$ ,

a = 1

$a = 1$ .

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Step 2.1

Rewrite the equation as

a {(1 - (0))}^{2} + 0 = 1

$a {(1 - (0))}^{2} + 0 = 1$ .

a {(1 - (0))}^{2} + 0 = 1

$a {(1 - (0))}^{2} + 0 = 1$

Step 2.2

Simplify

a {(1 - (0))}^{2} + 0

$a {(1 - (0))}^{2} + 0$ .

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Step 2.2.1

Add

a {(1 - (0))}^{2}

$a {(1 - (0))}^{2}$ and

0

$0$ .

a {(1 - (0))}^{2} = 1

$a {(1 - (0))}^{2} = 1$

Step 2.2.2

Subtract

0

$0$ from

1

$1$ .

a \cdot 1^{2} = 1

$a \cdot 1^{2} = 1$

Step 2.2.3

One to any power is one.

a \cdot 1 = 1

$a \cdot 1 = 1$

Step 2.2.4

Multiply

a

$a$ by

1

$1$ .

a = 1

$a = 1$

a = 1

$a = 1$

a = 1

$a = 1$

Step 3

Using

y = a {(x - h)}^{2} + k

$y = a {(x - h)}^{2} + k$ , the general equation of the parabola with the vertex

(0, 0)

$(0, 0)$ and

a = 1

$a = 1$ is

y = (1) {(x - (0))}^{2} + 0

$y = (1) {(x - (0))}^{2} + 0$ .

y = (1) {(x - (0))}^{2} + 0

$y = (1) {(x - (0))}^{2} + 0$

Step 4

Solve

y = (1) {(x - (0))}^{2} + 0

$y = (1) {(x - (0))}^{2} + 0$ for

y

$y$ .

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Step 4.1

Remove parentheses.

y = (1) {(x - (0))}^{2} + 0

$y = (1) {(x - (0))}^{2} + 0$

Step 4.2

Multiply

1

$1$ by

{(x - (0))}^{2}

${(x - (0))}^{2}$ .

y = 1 {(x - (0))}^{2} + 0

$y = 1 {(x - (0))}^{2} + 0$

Step 4.3

Remove parentheses.

y = (1) {(x - (0))}^{2} + 0

$y = (1) {(x - (0))}^{2} + 0$

Step 4.4

Simplify

(1) {(x - (0))}^{2} + 0

$(1) {(x - (0))}^{2} + 0$ .

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Step 4.4.1

Add

(1) {(x - (0))}^{2}

$(1) {(x - (0))}^{2}$ and

0

$0$ .

y = (1) {(x - (0))}^{2}

$y = (1) {(x - (0))}^{2}$

Step 4.4.2

Multiply

{(x - (0))}^{2}

${(x - (0))}^{2}$ by

1

$1$ .

y = {(x - (0))}^{2}

$y = {(x - (0))}^{2}$

Step 4.4.3

Subtract

0

$0$ from

x

$x$ .

y = x^{2}

$y = x^{2}$

y = x^{2}

$y = x^{2}$

y = x^{2}

$y = x^{2}$

Step 5

The standard form and vertex form are as follows.

Standard Form:

y = x^{2}

$y = x^{2}$

Vertex Form:

y = (1) {(x - (0))}^{2} + 0

$y = (1) {(x - (0))}^{2} + 0$

Step 6

Simplify the standard form.

Standard Form:

y = x^{2}

$y = x^{2}$

Vertex Form:

y = x^{2}

$y = x^{2}$

Step 7

Enter YOUR Problem

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$