Q1. Identify the vertex, focus, axis... [FREE SOLUTION]

Chapter 8: Q1. (page 423)

Identify the vertex, focus, axis of symmetry and directrix of the graph of the parabola $y = 4 {(x - 3)}^{2} - 7$ .

Short Answer

Expert verified

The vertex is $(3, - 7)$ . Focus is $(3, - \frac{111}{16})$ . Axis of symmetry is $x = 3$ . The equation of directrix is $y = - \frac{113}{16}$ .

Step by step solution

Step 1. Write down the given information.

The given equation is $y = 4 {(x - 3)}^{2} - 7$ .

Step 2. Concept used.

For two different forms of equations of parabola stated below, use the following key-concept to find vertex, axis of symmetry, focus, directrix, direction of opening of parabola and length of latus rectum.

Step 3. Comparing the given equation with standard form.

On comparing the equation $y = 4 {(x - 3)}^{2} - 7$ with standard form $y = a {(x - h)}^{2} + k$ , we get $a = 4, h = 3 and k = - 7$ .

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

The vertex and focus, the equations of the axis of symmetry and directrix of the parabola are evaluated as:

The vertex is $(3, - 7)$ .

Focus is evaluated as:

$\begin{matrix} (h, k + \frac{1}{4 a}) = (3, 鈭� 7 + \frac{1}{4 (4)}) \\ = (3, 鈭� \frac{111}{16}) \end{matrix}$

Axis of symmetry is $x = 3$ .

The equation for directrix is evaluated as:

$\begin{matrix} y = k 鈭� \frac{1}{4 a} \\ y = 鈭� 7 鈭� \frac{1}{4 (4)} \\ y = 鈭� \frac{113}{16} .... (Directrix) \end{matrix}$

Step 5. Conclusion.

The vertex is $(3, - 7)$ . Focus is $(3, - \frac{111}{16})$ . Axis of symmetry is $x = 3$ . The equation of directrix is $y = - \frac{113}{16}$ .

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Identify the vertex, focus, axis of symmetry and directrix of the graph of the parabola $y = 4 {(x - 3)}^{2} - 7$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Comparing the given equation with standard form.

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

Step 5. Conclusion.

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91影视

Identify the vertex, focus, axis of symmetry and directrix of the graph of the parabola y=4x-32-7.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Comparing the given equation with standard form.

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

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Applied Mathematics

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Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Identify the vertex, focus, axis of symmetry and directrix of the graph of the parabola $y = 4 {(x - 3)}^{2} - 7$ .