Chapter 9.5, Problem 74E

a.

To determine

To find: The correct option of the graph which matches with the given discriminant.

Answer to Problem 74E

The required correct option is C.

Explanation of Solution

Given information:

The discriminant: $b^2-4ac>0$

The options of discriminant:

A.

B.

C.

The given discriminant is $b^2-4ac>0$ .

The above discriminant of an quadratic equation indicates that the equation has 2 solutions which are real numbers.

This means the graph of the equation which has 2 real solutions has 2 x -intercepts.

So, the above discriminant matches with graph in option C.

Hence, the required correct option is C.

b.

To determine

To find: The correct option of the graph which matches with the given discriminant.

Answer to Problem 74E

The required correct option is A.

Explanation of Solution

Given information:

The discriminant: $b^2-4ac=0$

The options of discriminant:

A.

B.

C.

The given discriminant is $b^2-4ac=0$ .

The above discriminant of an quadratic equation indicates that the equation has 1 solution which is a real number.

This means the graph of the equation which has 1 real solution touches the x -axis on its vertex.

So, the above discriminant matches with graph in option A.

Hence, the required correct option is A.

c.

To determine

To find: The correct option of the graph which matches with the given discriminant.

Answer to Problem 74E

The required correct option is B.

Explanation of Solution

Given information:

The discriminant: $b^2-4ac<0$

The options of discriminant:

A.

B.

C.

The given discriminant is $b^2-4ac<0$ .

The above discriminant of an quadratic equation indicates that the equation has no solution which is a real number.

This means the graph of the equation which has no real solution does not touch or intersect the x -axis.

So, the above discriminant matches with graph in option B.

Hence, the required correct option is B.