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Warm Up: Review GCF and Factoring Sum of 2 Cubes

Warm Up: Review GCF and Factoring Sum of 2 Cubes. Hint: First GCF! Then, if necessary, Look at yesterday’s notes if you can’t remember how to factor sums of cubes. 16x 3 +54. Pick up 2 graphing grids – for your notes. F L I P V O C A B. Notes 5.3: Quadratic Equation Forms.

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Warm Up: Review GCF and Factoring Sum of 2 Cubes

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  1. Warm Up: Review GCF and Factoring Sum of 2 Cubes Hint: First GCF! Then, if necessary, Look at yesterday’s notes if you can’t remember how to factor sums of cubes 16x3+54 Pick up 2 graphing grids – for your notes

  2. F L I P V O C A B Notes 5.3: Quadratic Equation Forms Parent Function Standard Form Vertex Form Last lesson we studied Quadratics using the Parent Function and Vertex form (shifts). Today we will focus on the Standard form! Also: Study interval notation

  3. Kids should have this outline in their flip notes – tchr needs to discuss and fill in F L I P V O C A B Standard form: y = ax2 + bx + c If “a” is positive, the x parabola opens _______ If “a” is negative, the parabola opens _______ y intercept: where the parabola crosses the y axis. To find it from the equation, substitute ___ for ___ and solve for _____ up down 0 y x Min or max The vertex is the __________ point of the parabola. To find the x-coordinate: To find the y-coordinate: S/R/Z refers to : ____________________, _________, __________ These are the x-intercepts, so where y = _______. solution root zero Sub vertex x value in the eq. and solve for y 0 The Axis of symmetry is a fold line and has an equation: Domain: Possible __ values Range: Possible __ values x y

  4. Kids should have this outline in their flip notes – tchr needs to discuss and fill in Inequality / Set Builder/ Interval Notations Set Builder Interval Notation The domain is greater than -3 and less than or equal to 4 The domain is greater than 7 The range is less than or equal to 4 The range is all real numbers The domain is greater than -3 and less than or equal to 4 The domain is greater than 7 The range is less than or equal to 4 The range is all real numbers Discuss set builder notation vs. inequality notation

  5. Standard form: y = -x2 + x + 6 x – 3 x + 2 -1 ( ) ( ) Domain: Range: S/R/Z: Vertex: y • • • Axis of Symmetry: y-intercept: • • x y-int=(0,6)

  6. M A R K E R B O A R D ODDs = 4(x2 – 9 ) Standard form: f(x) = 4x2 – 36 x + 3 x – 3 4( ) ( ) Domain: Range: S/R/Z: Vertex: y -3 x 3 • • V(0,-36) Axis of Symmetry: x=0 • • y-intercept: y-int=(0,-36) -36 • 2 -20 -2 -20

  7. Standard form: f(x) = -2x2 + 10 x=± x2=5 Are the solution/root/zeros rational, irrational or imaginary? can’t be written as fractions of integers! S/R/Z: M A R K E R B O A R D EVENs Vertex: y V(0,10) • • x=0 Axis of Symmetry: y-intercept: y-int=(0,10) 1 8 -1 8 x • •

  8. Quadratic Inequality: f(x) How does the graph of this quadratic inequality compare to the graph of the quadratic equation? y Less than so shade below and solid on curve since it has an equal symbol as well • • • • •

  9. When are roots in a quadratic imaginary? Graph Equation When the graph does not touch the x-axis When solving the equation and the solution is the square root of a negative number

  10. Quadratic Application

  11. f(x) = -16x2 + 50 models the height of a rock dropped from a height of 50 feet. Exactly when does this rock reach the ground? The rock will reach the ground when y=0 0 = -16x2 + 50 16x2 = 50

  12. f(x) = -3x2 + 12x + 50 models the money earned by a business when they sell x widgets. Find the number of widgets which will produce the maximum amount of money. Also name the dollar amount. Vertex = max

  13. If the path of a ball is modeled by the equation Where (x) represent the time in seconds and (y) is the height in feet. A. Find the y-intercept and explain what it represents in this situation. Substitute “0” for x and solve for y The y-intercept represent the initial height of the ball before it is thrown/dropped.

  14. B. Find the vertex and explain what it represents in this situation. To find the vertex, you first must find the x-value by using the formula. Now plug this value in to your equation to find the y-value of the vertex. Vertex: The vertex represent that at 1 sec. the ball will at its maximum height of 64 ft.

  15. C. At what time will the ball reach the ground? Remember the ball is on the ground when y = 0, so plug zero (0) for “y” and solve the equation. Remember that factoring is the quickest way to solve a quadratic equation, so TRY THAT FIRST!! Our solutions represent the time the ball will hit the ground, you can not use the negative answer. Therefore, the ball will reach the ground in 5 sec.

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