Chapter 10: Q. 44 (page 644)

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
${(y + 1)}^{2} = - 4 (x - 2)$

Short Answer

Expert verified

The vertex is $(2, - 1)$ ,focus is $(1, - 1)$ and directrix is $x = 3$ .

Step by step solution

Step 1. Given information .

Consider the given equation ${(y + 1)}^{2} = - 4 (x - 2)$ .

Step 2. Analyze the equation .

The standard form of parabola is ${(y - k)}^{2} = 4 a (x - h)$

Compare the given equation with standard form.

${(y - k)}^{2} = 4 a (x - h) {(y + 1)}^{2} = - 4 (x - 2) 4 a = - 4 a = - 1 h = 2, k = - 1$

Further simplify.

Since the value of $a = - 1$ then the vertex is $(h, k) = (2, - 1)$ and focus is $(h + a, k) = (1, - 1)$ and the directrix is $x = h - a = 3$

Step 3. Plot the graph .

The graph of the equation by using graphing utility just shown below.

Here V is the vertex , F is the focus and line $x = 3$ represents directrix of the parabola .

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Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
${(y + 1)}^{2} = - 4 (x - 2)$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Analyze the equation .

Step 3. Plot the graph .

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Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.y+12=-4x-2

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Analyze the equation .

Step 3. Plot the graph .

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
${(y + 1)}^{2} = - 4 (x - 2)$