Chapter 3: Q. 10 (page 155)

True or False If the discriminant $b^{2} - 4 a c = 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will touch the x-axis at its vertex.

Short Answer

Expert verified

The given statement is true.

Step by step solution

Step 1. Given information.

The given statement is:

If the discriminant $b^{2} - 4 a c = 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will touch thex-axis at its vertex.

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

If the discriminant $b^{2} - 4 a c > 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will touch the x-axis twice.

If the discriminant $b^{2} - 4 a c = 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will touch the x-axis at one point and that point is its vertex.

If the discriminant $b^{2} - 4 a c < 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will not touch thex-axis.

Step 3. Conclusion.

The given statement is true.

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True or False If the discriminant $b^{2} - 4 a c = 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will touch the x-axis at its vertex.

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Conclusion.

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

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Geometry

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

True or False If the discriminant $b^{2} - 4 a c = 0$ , the graph of $f (x) = a x^{2} + b x + c, a \neq 0$ , will touch the x-axis at its vertex.