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Chapter 9: Q. 393 (page 977)

Describe the steps needed to solve a quadratic inequality graphically.

Short Answer

Expert verified

Write the inequality in standard form, then graph the function f(x)=ax2+bx+cand determine the solution from the graph.

Step by step solution

01

Step 1. Write the quadratic inequality in standard form.

The standard form of inequality is:

ax2+bx+c<0

In the standard form, the sign of inequality can be >,鈮�,鈮�.

02

Step 2. Graph the function f(x)=ax2+bx+c.

Axis of symmetry of f(x)=ax2+bx+cis-b2a.

Vertex of the parabola is -b2a,f-b2a.

The y-intercept is f(0).

Solve the equationf(x)=0 for x-intercepts.

Use axis of symmetry, vertex and intercepts to draw the graph of the parabola.

03

Step 3. Determine the solution from the graph.

If the inequality sign is >, then find the interval where the graph is above the x-axis and if the sign is 鈮�, then use the close brackets.

If the inequality sign is <, then find the interval where the graph is below the x-axis and if the sign is 鈮�, then use the close brackets.

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