Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation $y = x^{2} - 12 x + 20$ . Then find the length of latus rectum and graph the parabola.

Question

Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation $y = x^{2} - 12 x + 20$ . Then find the length of latus rectum and graph the parabola.

Accepted Answer

The vertex is $(6, - 16)$ . Focus is $(6, - \frac{63}{4})$ . Axis of symmetry is $x = 6$ . The equation of directrix is $y = - \frac{65}{4}$ . The direction of opening of parabola is upwards. The length of latus rectum is $1 unit$ .

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Algebra 2

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Short Answer

Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation $y = x^{2} - 12 x + 20$ . Then find the length of latus rectum and graph the parabola.

Step by Step Solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Convert the given equation to standard form.

Step 4. Evaluating vertex, focus, equations of axis of symmetry and directrix and direction of opening of parabola.

Step 5. Sketch the graph of the parabola.

Step 6. Conclusion.

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Algebra 2

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Short Answer

Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation y=x2-12x+20. Then find the length of latus rectum and graph the parabola.

Step by Step Solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Convert the given equation to standard form.

Step 4. Evaluating vertex, focus, equations of axis of symmetry and directrix and direction of opening of parabola.

Step 5. Sketch the graph of the parabola.

Step 6. Conclusion.

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Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation $y = x^{2} - 12 x + 20$ . Then find the length of latus rectum and graph the parabola.