Chapter 3: Q. 9 (page 155)

True or False The y-coordinate of the vertex of $f (x) = - x^{2} + 4 x + 5$ is $f (2)$ .

Short Answer

Expert verified

The given statement is true.

Step by step solution

Step 1. Given information.

The given statement is:

The y-coordinate of the vertex of $f (x) = - x^{2} + 4 x + 5$ is $f (2)$ .

Step 2. Determine whether the given statement is true or false.

The vertex of $f (x) = a x^{2} + b x + c$ is $(- \frac{b}{2 a}, f (- \frac{b}{2 a}))$ .

In the given function $f (x) = - x^{2} + 4 x + 5, a = - 1, b = 4, c = 5$ .

$\begin{array}{rcl} - \frac{b}{2 a} & = & - \frac{4}{2 (- 1)} \\ = & - \frac{4}{- 2} \\ = & 2 \end{array}$

The y-coordinate of the vertex of the given function is role="math" localid="1645862681108" $f (2)$ .

Step 3. Conclusion.

The given statement is true.

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True or False The y-coordinate of the vertex of $f (x) = - x^{2} + 4 x + 5$ is $f (2)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine whether the given statement is true or false.

Step 3. Conclusion.

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True or False The y-coordinate of the vertex of f(x)=-x2+4x+5is f(2).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine whether the given statement is true or false.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

True or False The y-coordinate of the vertex of $f (x) = - x^{2} + 4 x + 5$ is $f (2)$ .