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Chapter 3: Q. 10 (page 155)

True or False If the discriminant b2-4ac=0, the graph of f(x)=ax2+bx+c,a鈮�0, will touch the x-axis at its vertex.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Step 1. Given information.

The given statement is:

If the discriminant b2-4ac=0, the graph of f(x)=ax2+bx+c,a鈮�0, will touch thex-axis at its vertex.

02

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

If the discriminant b2-4ac>0, the graph of f(x)=ax2+bx+c,a鈮�0, will touch the x-axis twice.

If the discriminant b2-4ac=0, the graph of f(x)=ax2+bx+c,a鈮�0, will touch the x-axis at one point and that point is its vertex.

If the discriminant b2-4ac<0, the graph of f(x)=ax2+bx+c,a鈮�0, will not touch thex-axis.

03

Step 3. Conclusion.

The given statement is true.

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Most popular questions from this chapter

In Problems 25鈥�32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

(e)g(x)鈮�0(f)f(x)>g(x)(g)f(x)鈮�1

f(x)=-x2+3g(x)=-3x+3

A is used to help us to see the type of relation, if any, that may exist between two variables.

If h(x)=-3x+4,then

a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.

Match each graph to one the following functions.

f(x)=x2-1

An accepted relationship between

stopping distance, d (in feet), and the speed of a car, v (in mph), isd=1.1v+0.06v2 on dry, level concrete.

(a) How many feet will it take a car traveling 45 mph to stop on dry, level concrete?

(b) If an accident occurs 200 feet ahead of you, what is the maximum speed you can be traveling to avoid being involved?

(c) What might the term 1.1vrepresent?
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