Solving Quadratic Equations Chapter 9

Solving Quadratic Equations by Graphing I can solve quadratic equations by graphing.

Solving Quadratic Equations by Graphing Core Concepts (page 283 in Student Journal) Solving Quadratic Equations by Graphing Write the equation in standard form, ax2 + bx + c = 0 (or a form you are comfortable graphing). Graph the equation. Find the x-intercepts if possible.

Solving Quadratic Equations by Graphing Number of Solutions to a Quadratic Equation 2 solutions: the graph intersects the x-axis at 2 places 1 solution: the graph intersects the x-axis at 1 place (vertex is on the x-axis) no solutions: the graph does not intersect with the x-axis

Solving Quadratic Equations by Graphing Examples (page 284 in Student Journal) Solve by graphing. #1) x2 + 4x = 0 #2) -x2 = -2x + 1 #9) x2 + 4 = 0

Solving Quadratic Equations by Graphing Solutions #1) x = -4, x = 0 #2) x = 1 #9) no solution

Solving Quadratic Equations Using Square Roots I can solve quadratic equations using square roots.

Solving Quadratic Equations Using Square Roots Vocabulary (page 288 in Student Journal) square root: inverse operation of squaring

Solving Quadratic Equations Using Square Roots Core Concepts (page 288 in Student Journal) Number of Solutions to a Quadratic Equation 2 solutions: when x2 = d and d > 0 1 solution: when x2 = d and d = 0 no solutions: when x2 = d and d < 0

Solving Quadratic Equations Using Square Roots Examples (page 289 in Student Journal) Solve the equation. #1) x2 + 49 = 0 #2) x2 – 25 = 0 #3) x2 + 6 = 6 #5) 2x2 - 72 = 0 #9) 81x2 – 49 = -24 #15) (2x + 7)2 = 49

Solving Quadratic Equations Using Square Roots Solutions #1) no solution #2) -5, 5 #3) 0 #5) -6, 6 #9) -5/9, 5/9 #15) -7, 0

Solving Quadratic Equations by Completing the Square I can solve quadratic equations by completing the square.

Solving Quadratic Equations by Completing the Square Vocabulary (page 293 in Student Journal) completing the square: the process of changing the expression x2 + bx into a perfect square trinomial by adding (b/2)2 to x2 + bx

Solving Quadratic Equations by Completing the Square Core Concepts (page 293 in Student Journal) Completing the Square Divide b by 2 Square (b/2) from step 1 Add (b/2)2 from step 2 to x2 + bx Factor x2 + bx + (b/2)2

Solving Quadratic Equations by Completing the Square Examples (page 294 in Student Journal) Solve the equation by completing the square. #7) x2 – 8x = -15 #14) x2 + 14x – 10 = 0

Solving Quadratic Equations by Completing the Square Solutions #7) 3, 5 #14) -14.68, 0.68

Solving Quadratic Equations Using the Quadratic Formula I can solve quadratic equations using the Quadratic Formula.

Solving Quadratic Equations Using the Quadratic Formula Vocabulary (page 298 in Student Journal) Quadratic Formula: if ax2 + bx + c = 0, then x = (-b + sqrt(b2 - 4ac))/2a and (-b - sqrt(b2 - 4ac))/2a discriminant: the expression under the square root in the quadratic formula (b2 - 4ac)

Solving Quadratic Equations Using the Quadratic Formula Core Concepts (page 298 in Student Journal) Interpreting the Discriminant If the discriminant is… positive, then there are 2 solutions. zero, then there is 1 solution. negative, then there are no solutions.

Solving Quadratic Equations Using the Quadratic Formula Examples (pages 299 and 300 in Student Journal) Determine the number of solutions to the equation. #8) -x2 + 6x + 3 = 0 #9) x2 + 6x + 9 = 0

Solving Quadratic Equations Using the Quadratic Formula Solutions #8) 2 solutions #9) 1 solution

Solving Quadratic Equations Using the Quadratic Formula Solve the equation using the Quadratic Formula. #1) x2 – 10x + 16 = 0 #5) -3x2 + 5x – 1 = -7

Solving Quadratic Equations Using the Quadratic Formula Solutions #1) 2, 8 #5) -0.82, 2.49