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10-3 Solving Quadratic Equations

10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

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Page 1: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

10-3 Solving Quadratic Equations

Page 2: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Quadratic Function(y = ax2+bx+c)Quadratic Equation(ax2+bx+c=0)

Page 3: 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.

Page 4: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

A quadratic equation usually has two solutions, but it can also have one solution or no solution!

Page 5: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

A quadratic equation usually has two solutions, but it can also have one solution or no solution!

The solutions are the x-intercepts….

one solution

two solutions

no solution

Page 6: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

You can solve it by graphing, solving, factoring or by using the quadratic formula (section 10-6)

Page 7: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by graphing

Just graph the equation and identify the x-intercept(s).

Page 8: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by solving/factoringSolve(simplify) the equation.

Example: 774 2 x

The solution is 0.

7 704 2 x02 x

Page 9: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by solving/factoringSolve(simplify) the equation.

Example: 33153 2 x

The solution is ±4.

15 15483 2 x162 x162 x

Page 10: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by solving/factoringSolve(simplify) the equation.

Example: 1692 x

There is no solution.

9 972 x72 x

Page 11: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by solving/factoring

Factor the equation, then set each factor equal to zero and solve.Example: 0252 x

0)5)(5( xx05x 05x5x 5x

The solutions are ±5.

Page 12: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by solving/factoring

Factor the equation, then set each factor equal to zero and solve.Example: 0652 xx

0)3)(2( xx02x 03x

2x 3xThe solutions are -2 and -3.

Page 13: 10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)

Solving by solving/factoring

Factor the equation, then set each factor equal to zero and solve.Example: 1682 xx

16

04x 04x4x 4x

The solution is -4.

1601682 xx


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