Chapter 3: Q. 101 (page 158)

State the circumstances that cause the graph of a quadratic function $f (x) = a x^{2} + b x + c$ to have no x-intercepts.

Short Answer

Expert verified

The graph does not have x-intercept when $b^{2} - 4 a c < 0$

Step by step solution

Given information

We are given a quadratic equation of the form $f (x) = a x^{2} + b x + c$

Explanation

We know that discriminant of a quadratic equation $a x^{2} + b x + c$ is given by $b^{2} - 4 a c$ .When $b^{2} - 4 a c < 0$ then the graph of the function does not intersect x-axis. Hence the function has no x-intercept when $b^{2} - 4 a c < 0$

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State the circumstances that cause the graph of a quadratic function $f (x) = a x^{2} + b x + c$ to have no x-intercepts.

Short Answer

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Given information

Explanation

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State the circumstances that cause the graph of a quadratic function f(x)=ax2+bx+cto have no x-intercepts.

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

State the circumstances that cause the graph of a quadratic function $f (x) = a x^{2} + b x + c$ to have no x-intercepts.