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Chapter 6: Q. 463 (page 638)

For the function, f(x)=x2-7x+5, find

(a) whenf(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)=-7are x=3or4.

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

Step by step solution

01

Step 1. Given and explanation

We have f(x)=x2-7x+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.

02

Step 2. Simplifying the trinomial.

(a) We have f(x)=x2-7x+5.

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

-7=x2-7x+5

Adding 7both sides,

-7+7=x2-7x+5+7x2-7x+12=0

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

x2-7x+12=0x2-4x-3x+12=0x(x-4)-3(x-4)=0(x-3)(x-4)=0

Using the zero product rule gives us,

  1. x-3=0x=3
  2. x-4=0x=4

This shows that values are3,4.

03

Step 3. Substituting values in functions.

We have f(x)=x2-7x+5.

Putting x=3,4gives us,

  1. When x=3
    =(3)2-7(3)+5=9-21+5=14-21=-7
  2. When x=4
    =(4)2-7(4)+5=16-28+5=21-28=-7
04

Step 4.  Solution for part (b)

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

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