To find the x-intercept(s), substitute in <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Solve the equation.

Rewrite the equation as <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>8</mn><mo>=</mo><mn>0</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>8</mn></mstyle></math> using the AC method.

Consider the form <math><mstyle displaystyle="true"><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> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Write the factored form using these integers.

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>4</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set the factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

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

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set the factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to both sides of the equation.

The solution is the result of <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><mn>0</mn></mstyle></math> .

x-intercept(s) in point form.

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

To find the y-intercept(s), substitute in <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Solve the equation.

Remove parentheses.

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>6</mn><mo>⋅</mo><mn>0</mn><mo>+</mo><mn>8</mn></mstyle></math> .

Simplify each term.

Raising <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to any positive power yields <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify by adding zeros.

Add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

y-intercept(s) in point form.

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math>

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math>

List the intersections.

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math>

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