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4/6 Solving Quadratic Equations by Graphing

Last updated over 4 years ago
17 questions

Solving Quadratic Equations by Graphing

In the previous unit we graphed quadratic equations, this unit will focus on several ways in which we can solve quadratic equations. The first method we will use is graphing.

What You Will Learn:
*Solve quadratic equations by graphing.
*Use graphs to fi nd and approximate the zeros of functions.

Number of Solutions of a Quadratic Equation

A quadratic equation has:
• no real solutions when the graph of its related function has no x-intercepts
• one real solution when the graph of its related function has one x-intercept.
• two real solutions when the graph of its related function has two x-intercepts.

Solving Quadratic Equations by Graphing

  • Step 1 Write the equation in standard form, ax2 + bx + c = 0.
  • Step 2 Graph the related function y = ax2 + bx + c.
  • Step 3 Find the x-intercepts, if any. The solutions, or roots, of ax2 + bx + c = 0 are the x-intercepts of the graph.
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The solution(s) are : (answer format: x = _____ and x = _____)

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The solution is: (answer format: x = _____ )

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Finding Zeros of Functions

Recall that a zero of a function is an x-intercept of the graph of the function.
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The zeros of f are

Solve the equation by graphing.

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In Exercises 14–17, find the zero(s) of f.

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The zeros are

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The zeros are

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The zeros are