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Intermediate Algebra – Student Workbook – Second Edition 2013

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Lesson 5b - Solving Quadratic Equations<br />

Mini-Lesson<br />

Problem 1<br />

MEDIA EXAMPLE <strong>–</strong> HOW MANY AND WHAT KIND OF SOLUTIONS<br />

Use your graphing calculator to help you determine the number and type of solutions to each of<br />

the quadratic equations below. Begin by putting the equations into standard form. Draw an<br />

accurate sketch of the parabola indicating the window you used. IF your solutions are real<br />

number solutions, use the graphing INTERSECT method to find them. Use proper notation to<br />

write the solutions and the x-intercepts of the parabola. Label the x-intercepts on your graph.<br />

a) x 2 <strong>–</strong> 10x + 25 = 0<br />

b) -2x 2 + 8x <strong>–</strong> 3 = 0<br />

c) 3x 2 <strong>–</strong> 2x = -5<br />

How are Solutions to a Quadratic Equation connected to X-Intercepts of the parabola?<br />

If the quadratic equation ax 2 +bx+c = 0 has real number solutions x 1 and x 2 , then the x-<br />

intercepts of f(x) = ax 2 +bx+c are (x 1 , 0) and (x 2 , 0).<br />

Note that if a parabola does not cross the x-axis, then its solutions lie in the complex number<br />

system and we say that it has no real x-intercepts.<br />

Scottsdale Community College Page 210 <strong>Intermediate</strong> <strong>Algebra</strong>

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