Add <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> to both sides of the equation.

Complete the square for <math><mstyle displaystyle="true"><mn>7</mn><mo>-</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>4</mn><mi>x</mi></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Use the form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> , to find the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Consider the vertex form of a parabola.

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> into the formula <math><mstyle displaystyle="true"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Simplify the right side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Move the negative one from the denominator of <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Find the value of <math><mstyle displaystyle="true"><mi>e</mi></mstyle></math> using the formula <math><mstyle displaystyle="true"><mi>e</mi><mo>=</mo><mi>c</mi><mo>-</mo><mfrac><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn><mi>a</mi></mrow></mfrac></mstyle></math> .

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Move the negative one from the denominator of <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Substitute the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>e</mi></mstyle></math> into the vertex form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>e</mi></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> equal to the new right side.

Use the vertex form, <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>a</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>h</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>k</mi></mstyle></math> , to determine the values of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> .

Since the value of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> is negative, the parabola opens down.

Opens Down

Find the vertex <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mstyle></math> .

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

Substitute the value of <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> into the formula.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

The focus of a parabola can be found by adding <math><mstyle displaystyle="true"><mi>p</mi></mstyle></math> to the y-coordinate <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> if the parabola opens up or down.

Substitute the known values of <math><mstyle displaystyle="true"><mi>h</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>p</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>k</mi></mstyle></math> into the formula and simplify.

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

Do you know how to Find the Axis of Symmetry y-4x=7-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 | seven hundred thirty-three million forty-eight thousand sixty-four |
---|

- 733048064 has 2048 divisors, whose sum is
**21646891008** - The reverse of 733048064 is
**460840337** - Previous prime number is
**127**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 35
- Digital Root 8

Name | one billion five hundred sixty million eight hundred seventeen thousand five hundred thirty-six |
---|

- 1560817536 has 2048 divisors, whose sum is
**37589806080** - The reverse of 1560817536 is
**6357180651** - Previous prime number is
**79**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 42
- Digital Root 6

Name | four hundred thirty-six million nine hundred eighty-seven thousand five hundred two |
---|

- 436987502 has 8 divisors, whose sum is
**749121456** - The reverse of 436987502 is
**205789634** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 44
- Digital Root 8