Step: 1

[Original equation.]

Step: 2

The x -intercepts occur when y = 0.

Step: 3

0 = -7x ^{2} + 3x - 7

[Substitute 0 for y .]

Step: 4

Compare the equation with the standard form to get the values of a , b and c .

Step: 5

[Substitute a = -7, b = 3 and c = -7 in the discriminant.]

Step: 6

= -187

[Simplify.]

Step: 7

Since the discriminant is negative, the quadratic equation has no real solution.

Step: 8

So, the graph has no x-intercepts.

Correct Answer is : Zero

Step: 1

[Standard form of a quadratic equation.]

Step: 2

- x ^{2} - 4x = 3

[Original equation.]

Step: 3

- x ^{2} - 4x - 3 = 0

[Subtract 3 from each side.]

Step: 4

Sketch the graph of the related quadratic function y = - x ^{2} - 4x - 3 as shown below:

Step: 5

In the graph shown, the x -intercepts are - 3 and - 1.

Correct Answer is : - 3 and - 1

Step: 1

[Original equation.]

Step: 2

The x -intercepts occur when y = 0.

Step: 3

0 = - 3x ^{2} + 2x - 3

[Replace y with 0.]

Step: 4

Compare the equation with the standard form to get the values of a , b and c .

Step: 5

[Substitute a = - 3, b = 2 and c = - 3 in the discriminant.]

Step: 6

= -32

[Simplify.]

Step: 7

Since the discriminant is negative, the quadratic equation has no real solution.

Step: 8

So, the graph has no x -intercepts.

Correct Answer is : Zero

Step: 1

[Original equation.]

Step: 2

The x -intercepts occur when y = 0.

Step: 3

0 = - 6x ^{2} + 5x - 6

[Replace y with 0.]

Step: 4

Compare the equation with the standard form to get the values of a , b and c .

Step: 5

[Substitute a = - 6, b = 5 and c = - 6 in the discriminant.]

Step: 6

= -119

[Simplify.]

Step: 7

Since the discriminant is negative, the quadratic equation has no real solution.

Step: 8

So, the graph has no x -intercepts.

Correct Answer is : Zero

Step: 1

[Original equation.]

Step: 2

The x -intercepts occur when y = 0.

Step: 3

0 = x ^{2} + 4x + 4

[Replace y with 0.]

Step: 4

Compare the equation with the standard form to get the values of a , b and c .

Step: 5

[Substitute a = 1, b = 4 and c = 4 in the discriminant.]

Step: 6

= 16 - 16 = 0

[Simplify.]

Step: 7

Since the discriminant is equal to zero, the quadratic equation has only one solution.

Step: 8

So, the graph has one x -intercept.

Correct Answer is : One

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- Intercept