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10-3 Solving Quadratic Equations
Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)
The solution to a quadratic equation are the x-intercepts of its quadratic function.
A quadratic equation usually has two solutions, but it can also have one solution or no solution!
The solutions are the x-intercepts…. one solutiontwo solutionsno solution
You can solve it by graphing, solving, factoring or by using the quadratic formula (section 10-6)
Solving by graphing Just graph the equation and identify the x-intercept(s).
Solving by solving/factoring Solve(simplify) the equation. Example: The solution is 0.
Solving by solving/factoring Solve(simplify) the equation. Example: The solution is ±4.
Solving by solving/factoring Solve(simplify) the equation. Example: There is no solution.
Solving by solving/factoring Factor the equation, then set each factor equal to zero and solve. Example: The solutions are ±5.
Solving by solving/factoring Factor the equation, then set each factor equal to zero and solve. Example: The solutions are -2 and -3.
Solving by solving/factoring Factor the equation, then set each factor equal to zero and solve. Example: The solution is -4.
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The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)
Essential Question: How do you use the quadratic formula and the discriminant? Students will write a summary including the steps for using the quadratic.
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1) What does x have to be for 3x = 0? 1) What does x have to be for 3(x -2) = 0 2) What does x have to be for (x–2) (x+3) = 0.
Discriminant Recall the quadratic formula: x = -b ±√ b2 - 4ac 2a.
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