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"><mn>4</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>9</mn><mi>x</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>0</mn></mstyle></math> .

Factor by grouping.

For a polynomial of 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> , rewrite the middle term as a sum of two terms whose product is <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>c</mi><mo>=</mo><mn>4</mn><mo>⋅</mo><mn>5</mn><mo>=</mo><mn>20</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mo>-</mo><mn>9</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> plus <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math>

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

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

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

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

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

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

Add <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to both sides of the equation.

Divide each term by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi><mo>=</mo><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>4</mn><mi>x</mi><mo>-</mo><mn>5</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

x-intercept(s) in point form.

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><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"><mn>4</mn><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>9</mn><mo>⋅</mo><mn>0</mn><mo>+</mo><mn>5</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"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>9</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>5</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>5</mn><mo>)</mo></mrow></mstyle></math>

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mstyle></math>

List the intersections.

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><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>5</mn><mo>)</mo></mrow></mstyle></math>

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