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 | one billion four hundred seventy-eight million five hundred fifty-one thousand eight hundred twenty-seven |
---|

- 1478551827 has 8 divisors, whose sum is
**1990921680** - The reverse of 1478551827 is
**7281558741** - Previous prime number is
**101**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | two hundred fifty-nine million nine hundred twenty-seven thousand four hundred eighty-two |
---|

- 259927482 has 16 divisors, whose sum is
**521776512** - The reverse of 259927482 is
**284729952** - Previous prime number is
**271**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 48
- Digital Root 3

Name | one billion eight hundred sixty-six million nine hundred two thousand three hundred thirty-five |
---|

- 1866902335 has 4 divisors, whose sum is
**2240282808** - The reverse of 1866902335 is
**5332096681** - Previous prime number is
**5**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 43
- Digital Root 7