Chapter 6: Q. 463 (page 638)

For the function, $f (x) = x^{2} - 7 x + 5$ , find
(a) when $f (x) = - 7$
(b) Use this information to find two
points that lie on the graph of the function.

Short Answer

Expert verified

(a) The values when $f (x) = - 7$ are $x = 3 o r 4$ .

(b) Two points that lie on the graph are $(4, - 7), (3, - 7)$ .

Step by step solution

Step 1. Given and explanation

We have $f (x) = x^{2} - 7 x + 5$ .

To find the values when $f (x) = - 7$ , substitute this value in the equation and then simplify the equation.

Put the resulting values in the equation to find two points that lie on the graph.

Step 2. Simplifying the trinomial.

(a) We have $f (x) = x^{2} - 7 x + 5$ .

Putting the value of $f (x) = - 7$ gives us,

$- 7 = x^{2} - 7 x + 5$

Adding $7$ both sides,

$- 7 + 7 = x^{2} - 7 x + 5 + 7 x^{2} - 7 x + 12 = 0$

Since $- 7 x = - 4 x - 3 x$ and
$(- 4) (- 3) = 12$ , we can write this as,

$x^{2} - 7 x + 12 = 0 x^{2} - 4 x - 3 x + 12 = 0 x (x - 4) - 3 (x - 4) = 0 (x - 3) (x - 4) = 0$

Using the zero product rule gives us,

$x - 3 = 0 x = 3$
$x - 4 = 0 x = 4$

This shows that values are $3, 4$ .

Step 3. Substituting values in functions.

We have $f (x) = x^{2} - 7 x + 5$ .

Putting $x = 3, 4$ gives us,

When $x = 3$
$= {(3)}^{2} - 7 (3) + 5 = 9 - 21 + 5 = 14 - 21 = - 7$
When $x = 4$
$= {(4)}^{2} - 7 (4) + 5 = 16 - 28 + 5 = 21 - 28 = - 7$

Step 4. Solution for part (b)

As we know that $f (3) = - 4$ and
$f (4) = - 7$ , So the points that lie on the graph are $(3, - 7), (4, - 7)$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For the function, $f (x) = x^{2} - 7 x + 5$ , find
(a) when $f (x) = - 7$
(b) Use this information to find two
points that lie on the graph of the function.

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Simplifying the trinomial.

Step 3. Substituting values in functions.

Step 4. Solution for part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Probability and Statistics

Discrete Mathematics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

For the function, f(x)=x2-7x+5, find(a) whenf(x)=-7(b) Use this information to find twopoints that lie on the graph of the function.

Short Answer

Step by step solution

Step 1. Given and explanation

Step 2. Simplifying the trinomial.

Step 3. Substituting values in functions.

Step 4. Solution for part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Probability and Statistics

Discrete Mathematics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

For the function, $f (x) = x^{2} - 7 x + 5$ , find
(a) when $f (x) = - 7$
(b) Use this information to find two
points that lie on the graph of the function.