5.3 – solving quadratic equations by factoring. ex. 1 solve y = x 2 + 5x + 6 by factoring
TRANSCRIPT
5.3 – Solving Quadratic Equations by Factoring
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 OR x + 3 = 0
Ex. 1 Solve y = x2 + 5x + 6 by factoring.
x2 + 5x + 6 = y
x2 + 5x + 6 = 0
(x )(x ) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 OR x + 3 = 0
-2 -2
Ex. 1 Solve y = x2 + 5x + 6 by factoring. x2 + 5x + 6 = y x2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0x + 2 = 0 OR x + 3 = 0 -2 -2 x = -2
Ex. 1 Solve y = x2 + 5x + 6 by factoring. x2 + 5x + 6 = y x2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0x + 2 = 0 OR x + 3 = 0 -2 -2 -3 -3 x = -2
Ex. 1 Solve y = x2 + 5x + 6 by factoring. x2 + 5x + 6 = y x2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0x + 2 = 0 OR x + 3 = 0 -2 -2 -3 -3 x = -2 OR x = -3
Ex. 2 Solve x2 = 6x by factoring.
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
x = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
+6 +6
x = 0
Ex. 2 Solve x2 = 6x by factoring.
x2 = 6x
-6x -6x
x2 – 6x = 0
x(x – 6) = 0
x = 0 OR x – 6 = 0
+6 +6
x = 0 OR x = 6
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
(x – 4)(x + 5) = 0
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
(x – 4)(x + 5) = 0
x2 + 5x – 4x – 20 = 0
Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form
ax2 + bx + c = 0, where a, b, and c are integers.
x = 4 x = -5
-4 -4 +5 +5
x – 4 = 0 x + 5 = 0
(x – 4)(x + 5) = 0
x2 + 5x – 4x – 20 = 0
x2 + x – 20 = 0