Chapter 3: Q. 20 (page 174)

In Problems 20 and 21, find the quadratic function for which:
Vertex is $(- 1, 2)$ ; contains the point $(1, 6)$ .

Short Answer

Expert verified

The quadratic function is $f (x) = {(x + 1)}^{2} + 2$ .

Step by step solution

Step 1. Given information.

Find the quadratic function for which:

Vertex is $(- 1, 2)$ ; contains the point $(1, 6)$ .

Step 2. Find quadratic function.

The vertex $(h, k)$ and one point on the graph of a quadratic function are know, then we can write:

$f (x) = a {(x - h)}^{2} + k$

The given vertex is $(- 1, 2) so, h = - 1, k = 2$

now substitute these values into the equation:

role="math" localid="1646309755879" $f (x) = a {(x + 1)}^{2} + 2$

To determine the value of $a$ , use a fact that point $(1, 6)$ is on the graph.

So, $f (1) = 6$

Step 3. substitute the values.

$f (1) = a {(x + 1)}^{2} + 2 6 = 4 a + 2 4 = 4 a a = 1$

Substitute the value of $a$ into the function.

localid="1646642168668" $f (x) = a {(x - h)}^{2} + k f (x) = {(x + 1)}^{2} + 2$

Step 4. Conclusion.

The quadratic function is $f (x) = {(x + 1)}^{2} + 2$ .

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In Problems 20 and 21, find the quadratic function for which:
Vertex is $(- 1, 2)$ ; contains the point $(1, 6)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find quadratic function.

Step 3. substitute the values.

Step 4. Conclusion.

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In Problems 20 and 21, find the quadratic function for which:Vertex is -1,2; contains the point 1,6.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find quadratic function.

Step 3. substitute the values.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Decision Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 20 and 21, find the quadratic function for which:
Vertex is $(- 1, 2)$ ; contains the point $(1, 6)$ .